Preheat the oven to 300°F (150°C). Line two baking sheets with parchment paper and prepare a piping bag fitted with a round tip.
In a food processor, pulse the almond flour and powdered sugar together until well combined. Sift the mixture into a bowl to remove any lumps and set aside.
In a clean mixing bowl, whip the egg whites with the cream of tartar until frothy. Gradually add granulated sugar while continuing to whisk until stiff peaks form. Add the vanilla extract and nutmeg, mixing until just combined.
Gently fold the almond flour mixture into the meringue in three additions using a rubber spatula. Be careful not to overmix; the mixture should flow like molten lava and form a ribbon when drizzled from the spatula.
Transfer the macaron batter to the prepared piping bag. Pipe small rounds (about 1.5 inches in diameter) onto the lined baking sheets, spacing them about an inch apart.
Tap the baking sheets firmly on the counter to release any air bubbles and allow the piped rounds to rest for 30-60 minutes, or until they form a dry skin.
Bake one tray at a time in the preheated oven for 15-18 minutes, rotating halfway through. The macarons should be firm on the outside and not stick to your finger when lightly touched.
Remove from the oven and let the macarons cool completely on the baking sheets before transferring them to a wire rack.
In a mixing bowl, beat softened butter until creamy. Gradually add the powdered sugar and beat until well combined. Add milk, nutmeg, and a pinch of cinnamon, mixing until smooth. Adjust milk for desired consistency.
Match macaron shells of similar sizes, pipe a dollop of filling onto the flat side of one shell, and sandwich it with another shell. Press gently to ensure even distribution of the filling.
Allow the assembled macarons to sit in the fridge for a few hours or overnight to let the flavors meld. Serve chilled or at room temperature.
Notes
Allow the assembled macarons to rest for better flavor.