Panzanella

1 cup extra-virgin olive oil , divided

2 tablespoons red wine vinegar

1 teaspoon balsamic vinegar

1/4 cup finely chopped shallot s

1/2 cup loosely packed fresh basil leaves, torn

1/2 pound red cherry or grape tomatoes, halved

1/2 pound yellow cherry or grape tomatoes, halved

Kosher salt

Freshly ground white pepper

1 small red onion , finely chopped

1 garlic clove, minced

1 to 1 1/2 teaspoons dried crushed red pepper flakes

1 teaspoon fresh rosemary , chopped

1 (15-ounce) can cannellini bean s, drained and rinsed well

1 tablespoon fresh lemon juice

1 fennel bulb, thinly sliced

1/2 pound baby arugula

Pecorino cheese , crumbled