Bring a large pot of salted water to a boil over high heat. Cook the tortellini according to the package instructions. When fully cooked, drain and toss with 2 tablespoons of the olive oil and allow to cool to room temperature.
Meanwhile, in a nonreactive mixing bowl, combine the diced tomatoes, herbs, shallots, lemon juice, and remaining 1 1/4 cups olive oil. Mix to combine and season with gray salt and pepper to combine. When the tortellini have cooled to room temperature toss with the vinaigrette.
To serve, line the perimeter of a large serving platter with overlapping slices of the mozzarella. Spoon the tortellini salad in the center and scatter the arugula leaves over the top.
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