Step 1

For the dressing, place the shallots, olive oil, and vegetable oil in a small saucepan over low heat. Cook the shallots gently for 25 minutes, or until they are completely soft all the way through. Remove from the heat and allow them to cool to room temperature.

Step 2

Place the softened shallots, ½ cup of the oil, the vinegar, mustard, and salt in a small food processor. Pulse until the shallots are finely chopped and the dressing is thick. Set aside.

Step 3

To prepare the salad, bring a saucepan of salted water to a boil. Fill a bowl with water and ice, and set it aside. Add the green beans and wax beans to the boiling water and blanch until the color is bright and they are just losing their raw flavor, about 3 minutes. Drain and cool in the ice water.

Step 4

Bring another saucepan of salted water to a boil. Add the fregola to the boiling water and cook for 8 to 10 minutes, or until it is cooked through. Drain well and place in a large bowl. Add 1/3 cup of the dressing to the bowl and toss to coat. Allow the fregola to cool slightly. Drain the beans and add to the fregola along with the edamame, cherry tomatoes, tarragon, basil, and ½ teaspoon kosher salt; toss gently to coat. Divide the salad among 4 plates and serve topped with a burrata half and sprinkled with flake salt.