To begin, peel, halve, and core your apples (melon ballers make a good tool for coring halved apples). You’ll need one apple for every two tarts.
In a medium sauce pan, about 3 quarts (1 liter), slowly heat sugar. You’ll want to stir frequently until it dissolves into a brown syrup. Melt 1 tablespoon of butter into the sugar, stirring frequently. Add a dash of salt and the juice from ½ lemon.
Lower the heat as low as it will go and add your apple halves. Toss to coat with caramel and let simmer 5–10 minutes until tender, flipping once.
Cut puff pastry into circles to fit just within the top of your muffin tin.
Place apple halves curve-side down in a large muffin tin. Pour remaining caramel over each apple half. Top with a circle of puff pastry to fit just inside the muffin tin.
Bake 14–20 minutes at 450°F (230°C). Invert muffin pan onto baking sheet immediately. Serve with vanilla ice cream.