Make the blini: Place a wire rack over a baking sheet. Set aside.

In a large mixing bowl, gently whisk together the egg yolks, half and half, and 3 tablespoons of the melted butter.

In a small bowl, whisk together the almond flour, coconut flour, baking powder, and 3/4 teaspoon salt. Fold into the egg yolk mixture.

In the clean, dry bowl of a stand mixer fitted with the whisk attachment, whip the egg whites until light, white and fluffy, holding firm peaks, 2 to 3 minutes.

Gently fold the egg whites into the flour-egg yolk batter until combined. Do not overmix (you’ll get flat blini).

Heat a nonstick skillet over medium heat. Add 1 tablespoon of the melted butter. Spoon heaping teaspoons of batter into the pan about 1 inch apart, use a small spatula or back of a spoon dipped in melted butter to gently but quickly smooth and form each into a roughly 2 to 2 ½-inch disc and cook until golden, 1 to 2 minutes. Gently flip and repeat on the other side. Transfer the blini to the prepared wire rack. Repeat with the remaining butter and batter to make approximately 24 blini.

Make the mushroom and Gruyère topping: Heat the 2 tablespoons butter in a large, deep skillet over medium-high heat. Add the mushrooms and 1/2 teaspoon salt. Cook, stirring occasionally, until the mushrooms have released their liquid and the liquids have mostly evaporated, 10 to 15 minutes.

Stir in heavy cream and 1/4 teaspoon black pepper and bring to a boil. Reduce the heat to a simmer and stir in the cheese. Simmer until thickened slightly, 2 to 3 minutes. Stir in half of the thyme. Remove from heat.

To serve, arrange the blini on a platter. Top each with a spoonful of the mushrooms, and garnish with the remaining thyme.