Whisk soy sauce, canola oil, balsamic vinegar, sesame oil, and chili oil in a bowl until blended. Mix sugar, salt, ginger, and garlic into the same bowl, stir sauce to combine.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil. Cut red bell peppers in half from top to bottom; remove the stem, seeds, and ribs. Place peppers with cut sides down onto the prepared baking sheet.
Cook bell peppers under the preheated broiler until the skin of the peppers has blackened and blistered, 5 to 8 minutes. Place blackened peppers in a bowl and tightly seal with plastic wrap. Allow peppers to steam as they cool, about 20 minutes. Remove and discard skins, slice peppers into strips.
Fill a large pot with lightly salted water and bring to a rolling boil. Ease soba noodles into the water and return to a boil. Cook uncovered, stirring occasionally, until pasta is tender yet firm to the bite, 5 to 7 minutes. Drain.
Combine asparagus, scallions, red bell peppers, bean sprouts, sesame seeds, and cilantro in a large serving bowl. Add noodles and sauce, toss well to combine.