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To make the dough: In the bowl of a stand mixer fitted with the flat beater attachment, combine the flour, yeast, baking powder, sugar, and butter. Mix on low speed until the mixture is unevenly crumbly and the butter cubes have broken down with some larger chunks the size of walnuts remaining, about 2 to 3 minutes.
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In a small bowl, combine the water and salt; stir to dissolve the salt. Add it to the dry mixture and mix on low speed until all the ingredients are well combined, about 30 seconds. The dough will be very wet and the butter should now be in smaller chunks, roughly the size of peas. Let the dough rest for 10 minutes, uncovered, to allow the flour to hydrate. The mixture will become more cohesive but will still be quite sticky.
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Turn the dough out onto a lightly (gluten-free) floured surface and fold it over on itself until it comes together, about 3 to 4 times; a bench knife or bowl scraper is a helpful tool here. Use additional flour as needed to ensure the dough doesn’t stick to your hands or the work surface.
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Shape the dough into a rectangle, about 7" x 8" in size. Wrap in plastic or your favorite reusable wrap and refrigerate for 30 minutes.
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Place the chilled dough on a lightly floured piece of parchment. Roll the dough out on the parchment, aiming for a 13" x 18" rectangle. For the most refined look, trim all the sides with a bench knife or pizza wheel so the edges are straight; discard the scraps.
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Carefully transfer the rectangle of dough to a 13" x 18" baking sheet (a half-sheet pan), like the Crispiest Crust Pizza Pan, by pulling on the corners of the parchment and gently sliding it into the pan.
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Cover the pan and allow the dough to rise at room temperature for 1 hour, until the dough is visibly puffy around the edges. Toward the end of the rising time, preheat the oven to 425°F with a rack positioned in the center. While the crust rises, prepare the garlic-basil oil.
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To make the garlic-basil oil: In a small bowl, combine all of the ingredients. Set aside until the pizza is baked.
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To parbake the pizza: Transfer the crust to the center rack of the oven and bake for 12 to 14 minutes, until the surface looks matte and feels set. Some bubbles may form, and the crust will not take on much color at this stage. Don’t worry if the dough shrinks slightly while parbaking; that’s OK.
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Remove the crust from the oven and place the baking sheet on a cooling rack. Carefully spread the pizza sauce evenly over the parbaked crust, getting it nearly to the edges. Sprinkle the Parmesan over the sauce, then evenly distribute the shredded mozzarella followed by the cubed mozzarella.
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Return the topped pizza to the center rack of the oven and bake for 14 minutes, until the cheese is melted and lightly browned in spots; any exposed dough should be lightly golden brown.
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Remove the pizza from the oven. Using a bench knife, offset spatula, or Giant Spatula, slide the pizza out of the pan and transfer it to a wire rack or cutting board. Remove the parchment and slide the pizza back into the oven, directly on the center rack, for 4 to 6 minutes, until the sides and bottom are golden brown and crisp. Remove from the oven and transfer it to a wire rack.
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To finish the pizza: Sprinkle additional Parmesan cheese and drizzle about 1 to 2 tablespoons (12g to 25g) of the garlic-basil oil generously over the top. (Reserve the remaining oil for another use.) Let the pizza cool slightly on the rack, 3 to 5 minutes, before slicing and serving.
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Storage information: Store leftover Gluten-Free Sheet Pan in an airtight container in the refrigerator for several days. To reheat, wrap a single layer of slices in an aluminum foil packet. Heat in a 350°F oven until warmed through, about 10 minutes.
