Preheat oven to 350 degrees F. Grease a standard 9-inch pie plate with 1 tablespoon butter.
In a medium bowl, whisk together the eggs, milk, 3 1/2 tablespoons of the melted butter (reserving 1/2 tablespoon for later), vanilla, stevia and kosher salt.
Add the almond flour, whisking it until very smooth. Whisk in the baking soda.
Transfer the batter to the prepared pan. Use a spatula to spread evenly.
Place 7 apricot halves on top, cut side down, gently pressing them into the cake (the 8th apricot half is a bonus for the cook!). Brush the tops of the apricots with the remaining 1/2 tablepsoon of melted butter.
Bake the apricot cake until it's golden and fragrant, and a toothpick inserted in center comes out dry, about 30 minutes.
Remove the pan from the oven. Place on a wire rack to cool for about 20 minutes before slicing and serving.