Vegetarian Udon Noodles with Spicy Peanut Sauce

Name: Vegetarian Udon Noodles with Spicy Peanut Sauce
Ingredients: 16 ounces dry udon noodles (cooked according to package instructions and drained); 4 scallions (thinly sliced, white and light green parts separated); 2 ribs celery (with leaves; ribs sliced thinly on an angle and leaves roughly chopped); 4 small radishes (trimmed and thinly sliced into rounds); ⅓ cup creamy peanut butter; 3 tablespoons soy sauce; ⅓ cup unseasoned rice vinegar; 1 tablespoon (plus 2 teaspoons sesame oil, divided); 2 teaspoons chili oil (more or less to taste, depending on spice preference); 1 teaspoon toasted sesame seeds; Salt to taste; 2 eggs; More chili oil (optional)