Bring water to boil in the pot, then cook the pasta until ad dente, about 10 minutes. Drain.
While the water boils, heat the olive oil in the pan and add the chicken, cooking until it's almost cooked through, about 5 minutes. Season with salt and pepper.
Add the scapes and cook until the start to brown, about 3 to 4 minutes. Add the tomato halves and sauté until they brighten and just begin to release their juices, about 1 minute. Add the white wine and the basil leaves, cooking until the basil begins to wilt.
Toss the cooked pasta with the chicken and scapes until it's all thoroughly mixed. Divide among plates and served garnished with grated Parmesan cheese.