Preheat your oven to 375°F (190°C). Generously grease two 6-cavity donut pans with softened butter or nonstick spray, making sure to coat every crevice.

In a large mixing bowl, whisk together the milk, melted butter, egg, and vanilla extract until smooth and well combined.

In a separate bowl, whisk together the flour, granulated sugar, baking powder, salt, and nutmeg until evenly distributed.

Gently fold the dry ingredients into the wet ingredients using a rubber spatula. Stir just until no dry streaks remain — the batter should be slightly lumpy. Do not overmix.

Transfer the batter to a piping bag or large zip-top bag with the corner snipped off. Pipe the batter into the prepared donut pans, filling each cavity about two-thirds full.

Bake for 10-12 minutes, until the donuts spring back when lightly touched and a toothpick inserted comes out clean. Let cool in the pan for 5 minutes, then turn out onto a wire rack to cool completely.

While the donuts cool, make the caramel glaze. In a medium saucepan over medium heat, melt the butter. Add the brown sugar and heavy cream, whisking constantly. Bring to a gentle boil and cook for 2 minutes, whisking frequently, until slightly thickened.

Remove the caramel from heat and whisk in the powdered sugar, vanilla extract, and sea salt until completely smooth. Let cool for 2-3 minutes until the glaze thickens slightly but remains pourable.

Dip the top of each cooled donut into the warm caramel glaze, letting the excess drip back into the pan. Place glazed-side up on the wire rack and let the glaze set for 10 minutes before serving.