Grease the ramekins or mugs. In a microwave-safe bowl, melt the butter 30 to 40 seconds on high, then let it cool 1 minute.
Whisk in the cocoa powder, powdered sweetener, and salt until a thick glossy paste forms.
Add the eggs one at a time, whisking well after each. Whisk in the cream and vanilla until smooth and slightly aerated.
Divide the batter evenly among the three ramekins, filling each half to two thirds full.
Press one third of the chopped chocolate into the center of each portion, just below the surface.
Microwave one at a time on full power 60 to 100 seconds in a 1000 W microwave, starting at 60 seconds. The cake should pull from the sides and the center should look soft and slightly glossy. If needed, continue in 10 to 15 second bursts.
Rest 1 minute. Serve immediately. Optionally invert onto a small plate.