To Make the Coffee Sauce:

1. Combine coffee and syrup in a saucepan over medium heat. Bring to a low simmer, stirring occasionally, for about 4 minutes. Do not allow the mixture to boil.
2. Reduce heat to medium-low and simmer for 2 hours, until reduced by half.

To Make the Cakes:

1. Butter and lightly flour six 6- to 10-ounce ramekins. Tap out any excess flour.
2. In a small saucepan, bring two inches of water to a boil over high heat. In a large metal bowl set above the saucepan, combine butter, both types of chocolate, and ground coffee. You can also use a double boiler for this if you have one.
3. Reduce heat and let the water simmer as you slowly whisk the mixture until the chocolate is almost fully melted. Remove bowl from heat and continue to whisk until melted completely and thoroughly combined. Set aside to cool slightly.
4. In a separate large bowl, mix together eggs, yolks, and sugar with a hand mixer. Beat until light and fluffy, and pale in color, about 2-3 minutes on medium-high speed. Reduce speed to medium-low and slowly pour in the chocolate mixture. Continue to mix until just combined.
5. Shut off the mixer and add the flour. Mix on low speed until just combined. Do not overwork the batter.
6. Divide the batter evenly between molds, and line a baking sheet with parchment paper. Place molds on the baking sheet and refrigerate for at least 30 minutes, or until you’re ready to bake and serve, for up to 8 hours.
7. Preheat oven to 450˚F Place tray of refrigerated molds in the oven. Bake for 10 minutes, or until the tops and sides are cooked and dry, but the insides are soft and runny.
8. Using oven mitts, carefully invert each mold onto a plate and let it sit for 10 seconds, then lift up one corner of each ramekin and the cake should slip out. Drizzle about 1/2 teaspoon of coffee sauce over each cake, or more to taste.
9. Serve warm, with ice cream or sorbet on the side.