Preheat oven to 450°F.
Prepare 4 remakins by greasking them with butter and dusting the insides with cocoa powder. Tap out any excess cocoa powder.
In a mixing bowl, add butter, chocolate, and espresso powder and melt in microwave in 30 minute intervals mixing between each or using the double boiler method. Be careful not to burn the chocolate. Once chocolate is melted, set aside.
In a seperate bowl, combine 2 eggs, 2 egg yolks, sugar, and salt and beat with an electric mixer for 5 minutes on high speed until the egg yolks are thick and light yellow.
Pour the melted chocolate in the egg mixture and mix until mostly combined.
Add in all purpose flour and fold in until fully incoporated.
Divide the chocolate batter evenly into 4 ramekins. Place ramekins on a baking sheet and place in preheated oven for about 10-12 minutes. The outsides of the cakes should be firm and the top centers will still be soft and jiggle slightly.
Remove from oven and let the lava cakes cool in the ramekins for 1 minute. Then, invert onto plates and the lava cakes should easily release from the ramekins.