Preheat the oven to 350°F (177°C). Line a 12‑cup muffin pan with liners, plus two more for a 14‑15 cup yield. Set aside.

In a large bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg.

In a medium bowl, combine melted butter, brown sugar, and granulated sugar. Whisk in eggs and vanilla, followed by the milk.

Gently pour the wet mixture into the dry ingredients and stir until just combined—do not overmix. Fold in the chopped apple.

Fill the cupcake liners about ¾ full. Bake 21‑23 minutes, rotating the pan halfway through. Use a toothpick to test doneness; it should come out clean. Cool completely.

For the frosting: In a saucepan over medium‑heat, melt butter and sugar together, stirring constantly. Once smooth, add 3 Tbsp heavy cream and salt. Attach candy thermometer; boil until mixture reaches 230°F (110°C). Remove from heat.

Transfer caramel to a heat‑proof bowl; let cool 15‑20 minutes.

Add confectioners’ sugar and remaining 2 Tbsp heavy cream. Beat on medium‑low until ingredients are fully incorporated, then high for 1 minute. Let frosting rest 20‑30 minutes to thicken.

Pipe frosting onto cooled cupcakes using your piping tip of choice. Drizzle extra caramel and garnish with apple slices, if desired.

Store: at room temperature for up to 1 day, or refrigerate up to 5 days. Frosted or unfrosted cupcakes may be frozen up to 3 months; thaw overnight before frosting or serving.