Heat oven to 350°. Coat a jumbo muffin pan with nonstick cooking spray.
Combine butter and chocolate in a medium glass bowl. Microwave for 45 seconds, then stir until smooth.
Whisk in sugar, then egg and egg yolk. Whisk in vanilla and sift cocoa powder over mixture. Fold in cocoa with a rubber spatula; stir in mini chips. Divide among 6 prepared pan indents (1/4 cup in each), spreading tops level. Bake at 350° for 15 to 20 minutes, until tops are shiny.
Run a knife around edge of cakes; remove from pan. Cool a few minutes on a rack; transfer to plates. Top each with a scoop of ice cream; drizzle with chocolate sauce and serve.
