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1
Heat the broiler. Line a rimmed sheet pan with foil. Add the tomatoes, 1/4 teaspoon salt, and 1 tablespoon olive oil. Toss with your hands. Broil until charred, juicy, and slouchy. For my broiler, this took almost 15 or so minutes, but broilers vary widely. Check the sheet pan every 5 minutes, and pull them when they look good to you.
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2
While the tomatoes are cooking, butterfly the chicken breasts. Which is just a fancy way of saying: Horizontally halve the chicken breast almost all the way, but stop right before you reach the end, then open the chicken breast like a book. (It should still all be in one piece, but half the thickness that it originally was.) Cover the chicken breast with plastic wrap and use the flat side of a meat mallet (or a rolling pin or a skillet) to pound the chicken breast until it's about 1-centimeter (or just under 1/2-inch) thick. Repeat with the remaining chicken breast. Season both all over with the 1 teaspoon salt and 1 teaspoon black pepper.
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3
When the tomatoes are done broiling, dump them in a bowl. Add the mint and the remaining 3 tablespoons olive oil. Stir, taste, and adjust the salt as needed.
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4
Heat a cast-iron skillet over high heat. When it's very hot, add 1 tablespoon canola oil. Now add one chicken breast-it should sizzle loudly. Cook for 1 to 1 1/2 minutes per side, until browned all over and the chicken is cooked through. Repeat with the remaining canola oil and chicken breast.
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5
To serve, put each pan-seared chicken breast on its own plate. Evenly top with the tomato salad and burrata. Sprinkle with more salt and drizzle with more olive oil.
