In a bowl, combine the chicken, 1/2 cup pesto, red pepper flakes, and a large pinch of salt. Set your grill, grill pan, or skillet to medium-high heat. Grill the chicken until lightly charred and cooked through, turning halfway through cooking, about 10 to 12 minutes.
Meanwhile, make the dressing. In a large salad bowl, whisk together the olive oil, lemon juice, tahini or mayo, dijon, Worcestershire, parmesan, and a pinch each of red pepper flakes, salt, and pepper.
Bring a large pot of salted water to a boil. Boil the pasta to al dente, according to package directions. Drain. Add the hot pasta and 2 tablespoons pesto and toss vigorously to combine. Add the chicken, tossing to combine.
Season with freshly cracked pepper and salt. Serve warm or cold.