Preheat the oven to 450°F. Grease 4 (6 to 8 oz) ramekins well with butter. Set them on a sheet pan.
In a double boiler, melt the butter and chocolate. Whisk until smooth and set aside. Add the eggs, egg yolks, sugar, espresso powder, and salt to a mixing bowl. Use an electric mixer to whisk on medium-high speed for 2 minutes. Mix in the vanilla and coffee extracts.
Add the chocolate mixture to the eggs, plus the flour and cocoa powder. Use a regular hand whisk to combine. Whisk just until homogenous, trying not to overmix. Pour the batter into the prepared ramekins. Immediately bake for 12 minutes on the middle rack.
Meanwhile, for the rose water whipped cream…add the heavy whipping cream to a mixing bowl. Use an electric mixer on medium-high speed to whisk the cream until foamy. Add the powdered sugar. Continue to whip until soft peaks form. Mix in the rose water.
Prepare 4 plates. Use a kitchen towel to place a plate over top the ramekin and invert the cake out onto the plate (be careful not to burn yourself). Serve immediately with the whipped cream, powdered sugar, and rose petals over top.