Fill a large pot with lightly salted water and bring to a boil. Stir in penne and return to a boil. Cook pasta uncovered, stirring occasionally, until cooked through but still firm to the bite, about 11 minutes. Drain penne and place in a large serving bowl.

Heat olive oil in a deep skillet over medium-high heat. Cook and stir garlic in the hot oil until fragrant, about 30 seconds; add shrimp and cook until pink and opaque, about 2 minutes. Remove shrimp and set aside, reserving olive oil in skillet.

Add broccoli rabe and red pepper flakes to skillet; cook and stir until rabe is tender and bright green, about 5 minutes. Add cream of chicken soup, white wine, diced tomatoes, cooked shrimp, lemon juice, 1/4 cup chopped fresh basil, 1/2 cup grated Parmigiano Reggiano cheese, salt, and ground black pepper; cook and stir until tomatoes are heated through, about 2 minutes.

Toss shrimp and broccoli rabe mixture with penne in serving bowl; top with remaining 1/4 cup basil and 1/2 cup Parmigiano-Reggiano cheese.