In the bowl of a stand mixer fitted with the paddle attachment, combine 520 g (4 cups) Caputo Fioreglut Gluten-Free Flour, 12 g (4 teaspoons) instant yeast, 14 g (1 tablespoon) granulated sugar, and 12 g (2 teaspoons) kosher salt. Whisk together.
Add 480 g (2 cups) warm water and 42 g (3 tablespoons) extra-virgin olive oil. Mix on medium speed for 4 minutes. The dough will be soft and sticky.
Add 28 g (2 tablespoons) extra-virgin olive oil to a 9x13-inch pan and spread it around to coat the bottom. Transfer the dough to the pan.
Use well-oiled hands to press it out toward the edges. Gluten-free focaccia dough doesn't really stretch so you just want to keep patting it out to spread it out on the pan.
In a small bowl, whisk together 113 g (8 tablespoons) salted butter, 110 g (½ cup) light brown sugar, and 8 g (1 tablespoon) ground cinnamon.
Pour half of the cinnamon butter evenly over the dough, reserving the rest for after proofing. Using oiled hands, fold the dough into thirds like a letter. Fold one short end toward the center, then fold the other end over the top. Flip seam-side down. It's ok if it's not perfect, you just want to try to keep as much of the cinnamon filling contained in the dough as possible so you get a ribbon throughout it.
Carefully press the dough back out to fill the pan using oiled hands. Some of the cinnamon filling may ooze out and that's okay.
Cover and let rise in a warm spot for 1 to 1.5 hours, until doubled in size.
During the last 30 minutes of rising, preheat the oven to 425°F.
Gently rewarm the remaining cinnamon butter until pourable. Drizzle it over the top of the dough. Use oiled fingers to dimple the dough all over.
Bake at 425℉ for 23 to 26 minutes, until golden brown on top.
Let the focaccia cool for about 10 minutes. While it cools, make the cream cheese glaze. Beat together 57 g (2 oz) cream cheese and 28 g (2 tablespoons) unsalted butter until smooth. Add 40 g (⅓ cup) powdered sugar and mix until combined. Add 15 to 30 g (1 tablespoon) milkuntil the glaze is drizzleable. Stir in 2 g (½ teaspoon) vanilla extract
Drizzle or spread the glaze over the warm focaccia. Slice into 12 pieces and serve.