Heat a medium sauté pan over medium heat, add 2 tablespoons of the olive oil and heat through. Add the shallot and sauté until soft but not caramelized, about 3 minutes.
Add the peas and continue to sauté for an additional 3 minutes. The peas should still be fairly vibrant.
Remove from the heat then stir in the red wine vinegar and season to taste with salt and pepper.
Add the burrata to a serving bowl or plate. Spoon the pea mixture over the top and garnish with the remaining olive oil, black pepper and lemon zest. Arrange the bread around the sides and serve.