Remove the ends from the tomatoes. Cut in half and remove the seeds. Dice the tomatoes and place in a mixing bowl. You want to minimize the amount of extra liquid that ends up in the tomato mixture.
Finely mince the garlic or grate it on a microplane and add to the tomatoes.
Stack the basil leaves on top of each other and roll into a log shape. Use a sharp knife to thinly slice the basil roll-up (chiffonade). Add the basil to the tomatoes.
Drizzle the olive oil over the tomatoes and gently mix everything together to combine. Season with salt and pepper to taste.
Dice the mozzarella (you want very small pieces) and add it to the tomato mixture. Gently mix.
Place the phyllo cups on a serving platter. Use a spoon to portion the Caprese mixture into each of the cups until the are all filled.
Serve immediately.
Notes
If you want to prepare this dish ahead of time, make the tomato/basil mixture, cover and refrigerate. Dice the cheese, place in a bowl, cover, and refrigerate. When you're ready to serve, combine the cheese and tomato mixture, and then portion into your puff pastry cups.