In a medium bowl, whisk together the heavy cream, powdered sugar, vanilla bean paste, and salt until thickened but still smooth, one and a half to two minutes.

Cover and refrigerate until ready to serve.

Taste your raspberries: if sweet, use one tablespoon of sugar; if tart, use two tablespoons.

In a small saucepan over medium-low heat, combine raspberries, sugar, lemon juice, lemon zest, water, and salt. Mash with a fork or whisk to release the juices.

Cook three to five minutes, until the berries soften and the sugar dissolves.

Strain through a fine-mesh sieve into a bowl, pressing with a spoon to extract as much liquid as possible. Discard seeds. Taste and adjust sugar/salt as needed.

Cover and refrigerate to cool.

Preheat the oven to 450°F (232°C). Butter four (four-ounce) ramekins, then dust with cocoa powder, coating the bottom and sides. Assertively tap out excess to form a thin layer of cocoa powder. Place ramekins on a sheet tray.

In a heatproof glass bowl set over a small saucepan of simmering water (do not let bowl touch water), melt butter, chocolate, and espresso powder, stirring until smooth, about ten minutes. Remove from heat and stir in vanilla. Let cool slightly.

In the bowl of a stand mixer fitted with the whisk attachment, beat eggs, egg yolk, sugar, and salt on medium-high speed until doubled in volume, pale, and fluffy, four to five minutes.

Whisk flour into the chocolate mixture. Gently fold the chocolate mixture into the egg mixture, being careful not to deflate.

Divide the batter evenly among each ramekin. Then bake for nine to ten minutes, until cakes are risen, sides spring back when touched, and centers still jiggle slightly. Rest cakes in the ramekins for one minute.

To unmold: Place a small plate over each ramekin, wearing an oven mitt, invert quickly but gently, and let sit for ten seconds before lifting the ramekin off.

Dust the cakes with powdered sugar, garnish with mint, and serve with raspberry coulis and whipped cream.