Preheat the oven to 325 degrees F (165 degrees C). Line 18 muffin cups with paper liners.

Melt butter and chocolate chips in a saucepan over low heat, stirring until smooth, 3 to 5 minutes. Remove from the heat and let cool, 10 to 15 minutes.

Beat sugar and eggs in a mixing bowl with an electric mixer until thoroughly combined. Mix in flour and vanilla. Fold in cooled chocolate mixture until smooth. Spoon batter into the prepared muffin cups, filling each 1/2 full.

Bake in the preheated oven until a toothpick inserted into the center comes out clean or with a few moist crumbs, about 30 minutes.