Pour 360 ml / 1 1/2 cups apple cider into a 2-quart / 1.9 L saucepan and simmer over medium-high heat for about 15 minutes, until it reads 90 ml / 6 tbsp in a glass measuring cup and looks like thin maple syrup. Pull it early and the extra liquid loosens the batter and leaves the cake gummy.

Set the reduced cider aside to cool for 10 minutes. Meanwhile, heat the oven to 175 C / 350 F with a rack in the middle, brush the inside of a 10-cup / 25 cm bundt pan with the 1 tbsp softened butter, and dust it with the 2 tbsp flour, tapping out the excess.

Whisk the 300 g flour, baking powder, baking soda, salt, cinnamon, and nutmeg together in a 2-quart / 2 L bowl.

In a 4-quart / 4 L bowl, beat the 115 g softened butter with the brown and granulated sugars on medium speed for 3 minutes, until pale and fluffy. Beat in the eggs one at a time, then the vanilla.

Stir the sour cream, milk, and cooled cider together. Add the flour mixture to the butter mixture in three parts, alternating with the cider mixture in two parts, and mix on low just until no dry streaks remain. The batter will be thick and spoonable.

Scrape the batter into the prepared bundt pan, smooth the top, and tap the pan twice on the counter to settle it.

Bake for about 45 minutes, checking at 40, until the top is deep golden, a toothpick comes out with a few moist crumbs, and an instant-read thermometer reads 205 F / 96 C in the thickest part.

Cool the cake in the pan on a wire rack for 15 minutes. Loosen the edges with a thin spatula, invert onto the rack set over a sheet of parchment, and lift off the pan.

While the cake is still warm, stir the 100 g sugar and 1 1/2 tsp cinnamon together in a small bowl. Brush the cake all over with the 55 g melted butter, then spoon the cinnamon sugar over the top and sides, pressing it gently into the ridges. Slice with a serrated knife.