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Preheat the oven to 350°F with a rack in the center. Line two baking sheets with parchment.
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To prepare the filling: On one of the parchment-lined pans, spread the kataifi in an even layer. Toast in the oven for 5 to 8 minutes, until lightly browned and fragrant. Remove from the oven and set aside to cool while you prepare the rest of the filling.
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In a small saucepan, combine the butter, sugar, and heavy cream. Cook over medium-low heat, stirring occasionally, until the sugar has dissolved and the mixture comes to a boil, about 2 to 3 minutes after the butter has fully melted.
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Remove the saucepan from the heat and stir in the pistachio paste, almond extract, salt, chopped pistachios, and toasted kataifi. Set aside to cool at room temperature while you prepare the dough.
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To make the dough: In a small bowl, whisk together the flour, cocoa, baking powder, salt, and espresso powder.
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In a microwave-safe bowl or glass measuring cup with at least a 2-cup capacity, combine the butter and chocolate. Microwave in 30-seconds bursts at 50% power, stirring after each interval, until just melted and smooth, about 1 1/2 minutes total. Do not overheat.
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In the bowl of a stand mixer fitted the whisk attachment or in a large bowl working with an electric hand mixer, whisk together the sugars, eggs, and vanilla at medium-high speed until lightened in color and frothy, 3 to 5 minutes.
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With the mixer on low speed, slowly stream in the chocolate-butter mixture. Once it’s all added, stop the mixer and scrape the bowl, then mix again until fully combined.
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Using a flexible spatula, stir in the dry ingredients until just combined. If the dough seems too soft for scooping, let it rest, covered, for 15 to 20 minutes at room temperature. As the dough cools, the chocolate will become firmer, making the dough easier to scoop.
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To shape the cookies: Scoop the cooled filling into 1-tablespoon portions (about 15g to 20g each) onto one of the prepared baking sheets; a Tablespoon Scoop is a helpful tool here.
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Scoop the dough into 2-tablespoon portions (about 35 to 40g each); a 2-Tablespoon Scoop works well here.
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Working with one ball of dough at a time, use your greased hands to make an indentation about the size of a golf ball in the center, then place one of the balls of filling in side. Bring the cookie dough up and over the filling, pressing the edges together to completely enclose the filling. Roll the cookie between the palms of your hands to smooth out any cracks. If the dough is sticking, reapply a small amount of oil or nonstick spray to your hands as needed to make shaping easier.
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Repeat with the remaining dough and filling until all the cookies have been formed.
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Arrange the filled dough balls on the two parchment-lined pans, spacing them evenly apart. Using the palms of your hands, gently flatten each dough ball to about 1" thick.
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Bake the cookies on the center rack, one tray at a time, for 12 to 14 minutes. The cookies will be just set around the edges, while the centers will still look slightly underbaked. Remove from the oven and let the cookies cool completely on the pan. Repeat with the second pan.
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To garnish the cookies: When the cookies are completely cool, melt the chocolate in a glass measuring cup in the microwave, in 30-seconds bursts at 50% power until fully melted. Drizzle the melted chocolate over the cookies as desired, and sprinkle with the finely chopped pistachios. Let the cookies set at room temperature or in the refrigerator until the chocolate garnish is firm, about 15 minutes, before serving.
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Storage information: Store leftover Dubai Chocolate Cookies in an airtight container at room temperature for 3 to 4 days or freeze for longer storage.
