Butter a 9-inch spring form pan and line it with a circle of parchment paper. Set aside. Heat ½ cup whole milk until hot, then stir in the ½ cup poppyseeds. Set aside to steep.
In a medium-sized mixing bowl, whisk together the 1 ¾ cups oat flour , ½ cup almond flour , 1 teaspoon baking powder, 1 teaspoon baking soda, and ¼ teaspoon fine sea salt.
In a large bowl, using an electric mixer, beat the whites of the 3 large eggs until firm peaks form. In another large bowl, cream the ½ cup unsalted butter and 1 cup granulated sugar on medium-high speed until light and fluffy, about 3 minutes. Add the 2 teaspoons pure vanilla extract, then beat in the 3 egg yolks, adding one at a time and beating well after each addition. Scrape down the sides of the bowl with a rubber spatula as needed.
Drain the milk from the poppy seeds and discard the milk. Now beat in the poppyseeds and 1 cup Greek yogurt. Add the flour mixture to the batter in three additions, beating well after each addition. Scrape down the bowl, making sure it’s all well mixed.
Preheat the oven to 375ᵒF and rest the batter in the bowl while the oven heats. Then, fold in about a quarter of the beaten egg whites with the spatula, then fold in the remaining egg whites, mixing gently until just combined. Transfer the batter into the prepared cake pan, smoothing the top with the rubber spatula.
Place cake in the oven and bake until golden and firm, with the sides just beginning to pull away from the pan, and a tester inserted in the middle comes out clean, about 40-50 minutes. Remove from the oven and place on a wire rack. Carefully run a sharp, thin knife along the sides of the cake, just against the pan, then gently remove the rim and allow the cake to cool to room temperature before removing the base of the pan and slicing.
Notes
What type of pan? Madison suggests using a springform pan, so I did the same. However, I think you can just as well use a 9-inch round cake pan. Make sure to butter/grease it and line it with parchment paper.
Is that oven temperature high? The cake bakes at 375F which can be higher than some regular and gluten-free recipes. However, it is not a problem here, and the cake bakes evenly. If you think it's browning too quickly, tent foil over the top.
Make dairy-free. Swap softened coconut oil or your favorite non-dairy butter for the butter. Use your favorite non-dairy milk for the milk and your favorite non-dairy yogurt for the yogurt.
Bake as loaves. For a version of gluten-free poppyseed bread, bake this cake in a loaf pan or mini loaf pans.
Add a glaze. If you want a bit of sweet citrus contrast, glaze the cake with my simple lemon glaze.