Grilled Pesto Pizza with Marinated Mozzarella and Tomatoes

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6 cups fresh basil leaves

2 cups baby arugula 

1 cup grated Parmesan  

1/2 cup sliced almonds 

2 large cloves garlic, peeled 

Kosher salt 

Two 8-ounce containers marinated mozzarella balls, cut in half, plus 1 cup oil from the mozzarella (supplement with olive oil if needed)

2 tablespoons olive oil, plus for brushing 

1 1/2 pounds store bought pizza dough, at room temperature and divided into 3 balls 

1 1/2 pounds assorted color cherry tomatoes, sliced in half