Prepare the linguine per package instructions. Drain and rinse. Add 1 tablespoon olive oil and toss to coat.
Mix the spinach, green bell pepper, red bell pepper, red onion, green onions, cilantro, and jalapeno pepper with the linguine.
Whisk together 1/3 cup olive oil, rice vinegar or sherry, soy sauce, honey, lemon juice, lime juice, and minced garlic together in a bowl; pour over the noodle mixture and toss to coat. Sprinkle with black sesame seeds, if desired. Serve immediately or refrigerate until ready to serve.