Generously butter four 8-ounce ramekins with the softened butter and then, using a pastry brush, brush the butter on the sides of the ramekins in an upward direction; it will help the souffles rise. Dust the ramekins with 1 tablespoon superfine sugar, dividing it evenly among the ramekins.
In a medium saucepan, combine the raspberry liqueur, lemon juice, 1 cup raspberries and the remaining 2 tablespoons superfine sugar and bring to a simmer over medium heat. Cook until the raspberries have cooked down to a jam-like consistency, 3 to 4 minutes. Remove from the heat and let cool to room temperature.
Transfer 1 cup of the sauce to a large bowl and set aside. Reserve the rest in the pan.
Preheat the oven to 425 degrees F; position the rack in the middle.
Divide the remaining 1/4 cup raspberries among the ramekins and top evenly with the raspberry sauce from the pan. Set aside in the refrigerator until ready to use.
In the bowl of a stand mixer fitted with the whisk attachment, beat the egg whites on low speed until foamy, 1 minute. Add the cream of tartar and continue to beat on low speed for 1 minute. Raise the speed to medium and slowly add the powdered sugar. Continue to beat until the whites hold firm peaks, about 7 minutes. Fold a third of the beaten whites into the reserved 1 cup raspberry sauce to lighten it. Fold in the remaining egg whites. Spoon the souffle batter into the ramekins, smoothing it over if you want a tidy finish (see Cook's Note) or mounding it, like cotton candy, if you want a more rustic look. (If you are going for a classic souffle look, be sure to carefully and thoroughly wipe around the ramekin edges.)
Place the ramekins on a rimmed baking sheet and bake until the souffles are puffed and dark golden, about 15 minutes; they should remain pudding-like on the inside. Serve immediately, garnished with raspberries, if desired.
Don't level the souffle batter by swiping a spatula across. One side will often get stuck that way, and you'll get a lopsided souffle. Instead, lightly tap the souffle batter to level it. You might lose a few bubbles in the batter, but it'll rise.