Preheat your oven to 425°F. Butter six 6-ounce ramekins or six wells of a jumbo muffin pan. Place them on a baking sheet and lightly dust with flour, tapping out any excess.
In a medium saucepan, bring about 1 inch of water to a simmer over medium-high heat. Place the chocolate and 3/4 cup of butter into a heatproof glass bowl. Lower the heat to medium-low and set the bowl over the simmering water. Stir constantly until the chocolate and butter are fully melted. Remove the bowl from heat and let it cool for 5-10 minutes.
Once slightly cooled, stir in the powdered sugar and salt until the mixture is thick and well combined.
Add the eggs, egg yolks, and vanilla, stirring until fully incorporated. It may take a bit of mixing to get everything blended smoothly.
Sift the flour into the mixture, then gently stir and fold until fully combined.
Divide the batter evenly among the prepared ramekins or muffin wells, filling each about 2/3 full (approximately 1/2 cup per portion). If you're using ramekins, place them on a baking sheet before baking.
Bake in the preheated oven for 12 minutes, until the edges are set but the center remains soft.
Remove from the oven and let cool for 2 minutes. Run a knife around the edges to loosen them, then carefully invert onto dessert plates. If using a muffin pan, invert onto a cutting board or baking sheet, then transfer to individual plates.
Serve warm shortly after baking. If desired, garnish with ice cream, whipped cream, or fresh berries like raspberries or strawberries.