Preheat oven to 165°C (330F) and line an 8x4" loaf pan with parchment paper.
Sift and mix dry ingredients (flour, baking powder, baking soda, salt, ground cinnamon, ground nutmeg) and set aside.
Place granulated and brown sugar in a large mixing bowl of a stand mixer fitted with the paddle attachment. Add vegetable oil and mix until well combined.
Add vanilla extract and eggs, one by one, and mix for 1-2 minutes after each addition.
Add dry ingredients, alternating with apple cider, in two additions and mix until just combined. Do not overmix.
Pour batter into lined loaf tin and bake in a preheated oven for 50-70 minutes, or until a skewer inserted into the center comes out clean.
Allow cake to cool in loaf tin for 5-10 minutes, then transfer to a cooling rack. Whilst cake is still warm, use a pastry brush to brush the top of the cake with melted butter.
Mix granulated sugar and cinnamon in a small bowl. Sprinkle over top of cake brushed with melted butter.
Allow cake to cool, slice, and serve.