Preheat oven to 325 degrees F (165 degrees C). Line 18 cupcake cups with paper liners.
Melt butter and chocolate chips together in a saucepan over low heat, stirring until smooth; let cool.
Beat eggs and sugar together in a mixing bowl until thoroughly combined. Mix flour and vanilla extract into egg mixture. Fold in chocolate mixture until batter is smooth. Pour batter into prepared cupcake cups, filling them about 1/2 full.
Bake in the preheated oven until a toothpick inserted into the center of a cupcake comes out clean or with moist crumbs, about 30 minutes.