Preheat the oven to 350°F.
In a small food processor, combine the basil, mint, 5 tablespoons of the oil, the lemon zest and juice, and process until nearly smooth. Season to taste with salt. Leave the mixture in the food processor.
Heat a grill pan over medium-high heat. Drizzle 1 tablespoon of the oil over the ciabatta and season with salt. Grill the ciabatta for about 3 minutes per side, or until lightly toasted and grill marks form. Transfer to a plate.
Heat a medium heavy skillet over medium heat. Add the remaining
2 tablespoons oil, then add the shallot and garlic, and sauté for about
2 minutes, or until tender and translucent. Add the peas and cook for about 5 minutes, or until they are cooked through but still crisp-tender. Remove from the heat.
Add half of the warm pea mixture to the pesto and pulse until the peas are coarsely chopped. Transfer the mixture to a bowl and fold in the remaining warm pea mixture. Season with salt.
Divide the burrata among the bruschetta and season with salt and pepper. Spoon the pesto over, sprinkle with the Parmesan and serve immediately.