Preheat oven to 375°F.
Heat olive oil in a 10-inch oven-safe skillet or cast iron pan over medium heat.
Add the shallot and cook for 2–3 minutes until softened.
In a bowl, whisk together eggs, milk, salt, pepper, and chopped basil.
Scatter the heirloom tomatoes evenly over the shallots in the skillet.
Pour the egg mixture over the top.
Cook for 2–3 minutes without stirring, just until the edges begin to set.
Transfer the skillet to the oven. Bake for 20 minutes, or until the center is just set and the top is lightly golden.
Remove from the oven and let cool for a few minutes. Tear the burrata over the warm frittata so it becomes slightly melty.
Top with extra basil and serve warm or at room temperature.
