Preheat your oven to 375°F (190°C). Grease a madeleine pan with butter or non-stick spray.
In a bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt.
In another bowl, beat the eggs and sugar until pale and thick. Add the pumpkin puree and vanilla extract, and mix until combined.
Gently fold the dry ingredients into the wet ingredients until just combined. Fold in the melted butter.
Spoon the batter into the prepared madeleine pan, filling each mold about ¾ full.
Bake for 10 minutes, or until the edges are golden brown and the centers spring back when touched. Let cool in the pan for a few minutes, then transfer to a wire rack to cool completely.
For the chocolate dip, melt the chocolate chips and coconut oil in a microwave-safe bowl in 30-second intervals, stirring in between, until smooth.
Dip each madeleine halfway into the melted chocolate, then place on a parchment-lined baking sheet to set.