Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper. Toss the broccoli florets in olive oil and spread them out evenly on the baking sheet. Bake for 15 to 18 minutes or until tender and slightly charred.
While the broccoli is cooking, bring a pot of water to a boil. Add the dry soba noodles and cook according to package instructions, approximately 6 to 8 minutes. Drain and rinse the soba noodles with cold water.
Prepare the peanut sauce by whisking together the peanut butter, lime juice, rice vinegar, soy sauce, sesame oil, honey, garlic, and ginger. To thin out the sauce to your preferred consistency, add a small amount of water, whisk it up, and then add more as desired (½-1 cup total).
Transfer the noodles to a large mixing bowl, add the roasted broccoli, and use a vegetable peeler to shave a large carrot into thin strips over the bowl. Toss everything in the peanut sauce. Garnish with cilantro leaves to taste.
Store in an airtight container in the fridge for at least a half hour before serving. Or if you do not wish to serve it cold, you can enjoy immediately.