Preheat the oven to 350 degrees F (177 degrees C). Line the bottom of a 9 in (23 cm) springform pan with parchment paper. Grease the bottom and sides.
Melt the chocolate and butter together, in a double boiler on the stove or at medium-low power in the microwave, stirring occasionally. Do not overheat to avoid splitting.
Remove from heat and pour the chocolate mixture into a large bowl. Use a hand mixer to beat in the vanilla and sea salt at *low* speed.
Beat in the eggs at *low* speed, one at a time. Beat in the powdered sweetener, still at low speed. The mixture should be somewhat smooth, but a little lumpy.
Pour the batter into the lined pan. Smooth the top with a spatula. Place the springform pan onto a baking sheet to catch any leaks, just in case.
Bake for about 25 minutes, until the top just starts to form a very thin crust on the edges only, and the internal temperature in the center via thermometer is 140 degrees F (60 degrees C). The cake will not look done, which is normal, so go by the temperature.