In a large pot cook pasta in lightly salted boiling water for 5 minutes. Add the broccolini and cook for 3 minutes more or until pasta is done. Drain and run under cold water to cool completely. Drain again.
Meanwhile, in a large bowl whisk together the vinegar, oil, honey, garlic, and crushed red pepper, if using.
Add the pasta mixture, sweet pepper, onion, almonds, and basil to the vinegar mixture. Toss to combine. Gently stir in cheese. Season to taste.