Bring a large pot of salted water to a boil. Meanwhile, halve tomatoes lengthwise. Squeeze gently to remove most of seeds; discard seeds. Chop tomatoes into 1/2-inch pieces, and transfer to a bowl; set aside.
In a large skillet, heat oil over medium-low. Add shallots; cook until golden, stirring occasionally, about 5 minutes. Remove pan from heat. Stir in tomatoes until coated with oil; season generously with salt and pepper.
Cook pasta until al dente, according to package instructions. Drain; return to pot. Pour tomato mixture over pasta; add tarragon and Parmesan. Toss to combine. Divide among four bowls; top with additional Parmesan, if desired.