Whisk miso paste, canola oil, rice vinegar, orange zest, orange juice, ginger, mirin, peanut butter, and chile garlic sauce together in a bowl until dressing is blended.
Bring water to a boil in a large pot. Stir in soba noodles and return water to a boil. Boil noodles until tender, 5 to 8 minutes. Drain noodles in a colander under cold running water until cool, about 1 minute. Toss cooked soba noodles with 1/2 of the miso dressing in a large bowl until thoroughly coated.
Divide spinach among 4 serving bowls; top each with 1/4 of the dressed noodles. Divide carrots, cabbage, snow peas, and cherry tomatoes among each bowl; top each with 4 shrimp. Drizzle remaining miso dressing onto each bowl to taste; sprinkle with green onions and toasted sesame seeds.