Preheat oven to 375°F. Line a baking sheet with aluminum foil. Lay out the chicken on the lined sheet, drizzle with the olive oil, and sprinkle with the herbs, crushed pepper, and salt and pepper. Bake for 12-15 minutes, or until the chicken juices run clear and the internal temperature reaches 165°F.
While the chicken bakes, bring a large pot of salted water to boil over high heat. Cook the pasta to al dente, usually 1 minute less than the package directions indicate. Drain and rinse the pasta.
While the chicken and pasta are cooking, prep the rest of the salad. Start with the dressing: in a food processor, pulse the almonds until they are the size of coarse crumbs. Add the red pepper, garlic, salt, and lemon juice and process until everything just starts to come together. Add the 1/4 cup olive oil and process until nice and smooth - this shouldn't take too long. You're welcome to leave the dressing a little chunky if you'd like. Chop the cucumber into 1/2 inch chunks, roughly chop the olives. The chicken and pasta should be done right around this time.
Assemble the salad by tossing the still slightly warm but well drained pasta with the red pepper sauce, cucumber, olives, and cheese. Stir well, adding a drizzle of olive oil here and there to help break up the sauce evenly throughout the pasta. This is a good point to refrigerate the salad if needed.
This salad is definitely best at room temperature, so you'll want to take it out of the fridge about 20 minutes before serving it. Toss in the fresh basil just before serving with the greens, thinly sliced chicken, and salt and pepper to taste. Enjoy!