Preheat the oven to 425°F. Line a baking sheet or leave unlined if preferred.
Place 2 to 3 cups broccoli florets on the baking sheet. Drizzle with 1 tablespoon toasted sesame oil and sprinkle with a pinch of salt, a pinch of black pepper, and a pinch of crushed red pepper flakes. Toss to coat and spread the broccoli in a single layer.
Roast the broccoli in the preheated oven for 15 to 20 minutes, until slightly charred.
While the broccoli is roasting, bring a large pot of salted water to a boil. Remove and discard the flavor packets from the 2 (3-ounce) packages ramen noodles, then add the noodles to the boiling water and cook about 3 minutes (until tender). Drain the noodles well.
While the water is heating and/or the noodles are cooking, make the sauce: in a large skillet or saucepan, heat 3 tablespoons sesame oil over medium-low heat. Add 2 minced garlic cloves and 1 teaspoon freshly grated ginger and cook, stirring, for 1 minute until fragrant.
Stir into the skillet 1/3 cup peanut butter, 1/4 cup soy sauce, 1/4 cup warm water, 1 tablespoon chili garlic sauce, 1 tablespoon fresh lime juice, and 1 teaspoon honey. Stir continuously until the sauce is smooth and combined, lowering heat to keep it warm if needed.
Add the drained noodles to the sauce and toss to coat evenly.
Add 1 thinly sliced red bell pepper, 3 thinly sliced green onions, 1/4 cup chopped peanuts, 3 tablespoons chopped fresh cilantro, and the roasted broccoli to the noodles. Toss everything together until well combined.
Serve immediately.