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Preheat the oven to 350°F. Prepare an 8" square pan with a parchment sling or reusable silicone liner, then lightly grease the sides of the pan. Alternatively, line a 9" cake pan with a round piece of parchment or round reusable liner and lightly grease the sides.
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To make the crumbs: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a medium bowl, whisk together the flour, sugars, cinnamon, and salt. Add the butter and vanilla; toss to combine. Using a bowl scraper, a fork, or your fingers, work in the butter until crumbs form and no dry spots remain. The crumbs should be irregular, ranging in size from a pea to walnut. Set aside.
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To make the cake: In a large bowl or bowl of a stand mixer, combine the flour, sugar, baking powder, salt, and baking soda. Add the butter and mix at low speed using an electric hand mixer or the flat beater attachment of the stand mixer, until the mixture looks sandy, about 1 to 2 minutes. (This mixing method is called reverse creaming and is also known as the paste method.)
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Beat in the vanilla and egg, then mix until no dry spots of flour remain. Stop the mixer and scrape the bowl and beater attachment as needed; the mixture will be thick.
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If using buttermilk, slowly pour it into the mixture while the mixer is running on low speed. If using Greek yogurt, add the yogurt all at once before starting to mix. Continue to stir until smooth, then stop the mixer to scrape the bowl and mix again at medium-low speed for 1 minute; this final mix is key to ensuring the best texture so don't skip it.
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To assemble and bake the coffee cake: Transfer the batter into the prepared pan and spread it evenly all the way to the edges. (A small offset spatula is a helpful tool here.)
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Sprinkle the crumbs evenly over the batter and gently press to adhere.
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Bake the cake for 28 to 32 minutes, until it's set in the middle and the crumbs are golden brown. When the cake is done, a toothpick or paring knife inserted into the center should come out mostly clean. (You’ll have to poke through a layer of baked crumbs on top, but it’s helpful to check the cake's texture for doneness.)
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Remove the cake from the oven and allow it to cool in the pan for 20 minutes. If making the glaze, prepare it while the coffeecake is cooling.
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To make the glaze: In a small bowl, stir together the glaze ingredients until smooth, starting with smaller amount of water. Add additional water as needed until the glaze is the consistency of molasses.
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Remove the cake from the pan using the overhanging edges of parchment as handles to gently lift it out. (If you used a silicone liner or parchment round, run a nylon spreader or dull knife around the edges of the pan to loosen the cake and then gently tip it out.) Place the cake, still on the parchment if a sling was used, on a wire rack to cool slightly.
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Drizzle the glaze over the cake, or finish by dusting with non-melting sugar or confectioners’ sugar.
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Storage information: Store leftover coffee cake, well wrapped, at room temperature for several days; freeze for longer storage.
