Instructions
Step 1
To a medium pot, add the lemon juice, olive oil, ¾ teaspoon of the salt, the artichokes, and 4 cups of water and bring to a boil. Turn the heat to medium-low and simmer until the artichokes are tender when pierced with a knife, about 30 minutes. Remove from the heat (leaving the artichokes in the liquid).
Step 2
In a separate medium pot over medium heat, melt the butter. Add the mushrooms and cook, stirring occasionally, until softened and their liquid has evaporated, about 10 minutes. Add the cognac and cook until evaporated, about 30 seconds. Add ¼ cup of the cream, the parsley, tarragon, black pepper, and remaining salt and bring to a boil. Stir in the dissolved potato starch and continue boiling until thickened, about 1 minute more. Remove from the heat.
Step 3
Position a rack in the top third of the oven and preheat the broiler to high. Using a slotted spoon, transfer the artichokes, cavities facing up, to a parchment-lined baking sheet. Using a stand or handheld mixer, beat the remaining cream to stiff peaks and scrape into the mushroom mixture; working quickly, use a silicone spatula to gently incorporate. Spoon the mixture evenly into the artichoke cavities, sprinkle evenly with Pecorino, and broil until browned, 1–3 minutes. Serve warm.