Heat the oil in a saute pan and gently cook the garlic and onions until soft. Add the red peppers, 2/3 cup/150 ml of the stock and the tomato paste. Season with salt, black pepper and piment d'espelette. Simmer until the vegetables are tender and the liquid has completely evaporated. Puree with an immersion blender and transfer to a metal or glass bowl.
Stir the gelatin into the remaining stock in a small saucepan and heat, stirring to dissolve. Mix it well into the puree. Set the mixture on a bed of ice and cool until the mixture mounds when dropped from a spoon. Check the seasonings, adding lemon for acidity if needed. (The mixture should be highly seasoned because the cream, once added, will dilute the taste a bit.)
Whip the cream and gently fold it in. Pour the mixture into a mold, cover and chill until serving, at least 4 hours.