Brown the butter. Set out a medium heat-proof bowl. Slice the butter into tablespoon-sized pieces and place in a light-colored skillet over medium heat. Stir or whisk constantly. The butter will melt, then foam, then after 5–7 minutes you'll see lightly browned specks form at the bottom and smell a nutty aroma. Once the butter reaches a light caramel-brown color, immediately remove from heat and pour into the bowl, scraping in all the browned bits. Measure out 2 tablespoons and set aside for greasing the pans. Cool the remaining brown butter (about 1/2 cup) in the refrigerator for 30 minutes until room temperature and no longer warm. Do not cool longer or it will solidify.
Prep the pans. Preheat the oven to 350°F (177°C). Using a pastry brush, coat every cup of a 24-count mini muffin pan with the reserved 2 tablespoons of brown butter. Grease a second pan or plan to bake in batches since the recipe yields 30–36 cakes.
Make the batter. Using a hand mixer or stand mixer fitted with a whisk attachment, whip the egg whites on high speed until soft peaks form, about 2–3 minutes. Add the almond flour, all-purpose flour, granulated sugar, baking powder, salt, and lemon zest. Beat on low speed until combined - the batter will be sticky, lumpy, and thick, and the egg whites will deflate. That is fine! Pour in the vanilla extract and cooled brown butter and beat on low speed until the batter is smooth and combined.
Fill the pan. Spoon about 2 teaspoons of batter into each greased muffin cup. Lightly press one berry into the center of each cup. No need to submerge it - just nestle it on top.
Bake. Bake for 14–16 minutes until the edges are golden brown. Remove from the oven and cool in the pan for 10 minutes before removing. Tea cakes will slightly deflate as they cool - this is normal.
Dust and serve. Use a fine mesh sieve or sifter to dust confectioners' sugar over warm or cooled tea cakes before serving.
Store. Tea cakes are best the day they are made. Store leftover tea cakes loosely covered at room temperature for up to 3 days or in the refrigerator for up to 1 week.