Bring a pot of water to a boil. Add soba noodles, stir often, and cook according to package instructions until tender. Drain noodles and rinse under cold running water. Drain and set aside.
In a skillet, heat 1 Tbsp vegetable oil over medium-high heat. Season shrimp generously with salt and black pepper. Once skillet is hot, add shrimp. Turn shrimp over just once, cooking until pink, about 2-3 minutes. Set aside.
In a large bowl, combine soba noodles, snap peas, carrots, and green onions. Add sauce as much or little sauce as desired. Before serving, add cooked shrimp and toasted white sesame seeds. Serve warm, chilled, or at room temperature.
To make sauce: whisk together soy sauce, rice vinegar, honey, and sesame oil. Add freshly ground black pepper to taste.