Preparation

Make the basil oil

• Line a strainer with a double thickness of damp cheesecloth and place it over a bowl. Have ready a colander and a bowl of ice water. Bring a medium pot of water to a boil. Stir in the basil leaves and cook until bright green, about 10 seconds. Drain the basil in the colander and transfer to the ice water to cool. Squeeze out excess water, and pat dry with paper towels.
• In a blender, purée the basil with the canola oil until smooth. Pour into the lined strainer and let sit, undisturbed, until the oil is completely strained, about 30 minutes.

Prepare the other layers and assemble

• In a large bowl, toss the tomatoes with 1 Tbs. basil oil, 1/2 tsp. salt, and 1/4 tsp. pepper.
• In a small bowl, combine the onion, capers, and sun-dried tomatoes.
• Put 2 tsp. basil oil in each of eight 8- to 10-oz. flat-bottomed glasses. Top with a piece of burrata. Divide the onion mixture among the glasses, then layer on the mozzarella, balsamic glaze, tomato mixture, and olives. Top with two breadstick halves and the pea shoots, if using, and serve.

Make Ahead Tips

The basil oil will keep, refrigerated, for up to 1 week.

The verrines can be assembled (minus the garnishes) 2 to 3 hours ahead and refrigerated. Garnish with the breadstick halves and pea shoots just before serving.