Heat oven to 425°F. Butter 6 ramekins or spray with non-stick cooking spray. Place on to a baking sheet, then set aside.
Microwave chocolate and butter in medium microwaveable bowl on HIGH for 1 minute, or until butter is melted. Vigorously stir until chocolate is completely melted. If needed, microwave an additional 15 seconds,until the chocolate is melted. Cool slightly.
In a large mixing bowl, whisk eggs and egg yolks until fully combined. Beat in powdered sugar and vanilla extract.
Beat in butter and chocolate mixture until well blended.
Stir in flour, salt and espresso powder, by hand, until just combined.
Divide batter equally between ramekins (about 1/2 cup if using 6 oz. ramekins) and place them, evenly apart, on a baking sheet.
Bake for 12 to 14 minutes or until the edges of the cakes are firm but centers are still soft. Let stand for 1 min.
Carefully run knife around cakes to loosen; invert into dessert plates. Serve warm topped with ice cream, whipped cream, fruit or powdered sugar.