Place butter and chocolate in a bowl together and microwave them in about 30 second increments. You can also place them together and melt over a double boiler. Once fully melted, set aside to cool to room temperature.
Next, you want to place your eggs in a medium to large bowl. Begin whisking for a few minutes. You can also use a stand mixer with the whip or paddle attachment. After whisking for a few minutes, add in your sugar all at once and whisk until the mixture becomes thicker and paler in color. Whisking by hand it took about ten minutes. By machine, it should only take about five or six minutes.We're mixing the eggs and sugar until a "ribbon" consistency. Once it reaches the appropriate "ribbon stage" where the mixture forms a ribbon stream of egg mixture when you lift the paddle or whisk up, then you can whisk in the instant coffee granules, vanilla and oil. Whisk in for just a minute or two.
Now, pour in all your melted chocolate all at once. At this point the chocolate should be about room temperature before adding in. Whisk until combined.
Next, dump in the flour all at once. Begin to gently fold in the flour until just combined. Don't overmix!
Now your batter should be all ready to go. Just note that the lava center will be more fudgy. If you want it in a slightly more liquid form, add the appropriate amount of milk to the batter, along with the oil, vanilla, salt and coffee granules and mix in.
Prep your ramekins by buttering them well. Place about a tablespoon of flour or cocoa powder in each and tap around the inside the ramekin until it's well coated with butter and flour or cocoa power. Tap out the excess. Prep a baking sheet with parchment paper or a silicone liner. I like do that just in case anything spills over, however you can use a plain baking sheet. There shouldn't be an issue. Place your ramekins onto the baking sheet.
Preheat your oven to 375°F. Pour your chocolate cake batter into each ramekin as evenly as you can. Once both ramekins are filled, gently tap onto table or baking sheet and shake to remove excess air bubbles.
Bake at 375°F for about 7-9 minutes. The outer edges should appear baked, but the center should still be slightly jiggly.
Let the cakes cool for only a couple of minutes in the ramekin. After two minutes, carefully invert onto a plate. Be careful, it will still be hot. Key point: once you invert onto a plate, do not lift up to unmold until after a couple of minutes. If you don't wait those two minutes, then they won't unmold properly.
After unmolding the cake, you can enjoy, decorate as you please and enjoy warm!