Fill a large pot with lightly salted water and bring to a rolling boil. Ease soba noodles into water and return to a boil. Cook uncovered, stirring occasionally, until noodles are tender yet firm to the bite, 5 to 7 minutes. Drain and rinse with cold water.
Heat canola oil in a saucepan over medium heat; add onion, garlic, and ginger. Cook and stir until onions are translucent, 3 to 4 minutes. Add carrots, red bell pepper, and half the scallions to the pan; cook and stir to desired tenderness, 3 to 5 minutes.
Mix soy sauce, peanut butter, sesame oil, hot sauce, and brown sugar in a large bowl until peanut butter is incorporated. Add cooked soba noodles, cooked vegetables, and cucumber to the bowl; toss until fully combined with sauce. Add rice vinegar and toasted sesame seeds to the bowl, toss again. Chill for 30 minutes or more; garnish with remaining scallions and serve with lime wedges.