Cook the Noodles: Bring a large pot of salted water to a boil. Add the soba noodles and cook according to package instructions, usually 4 to 5 minutes. Stir occasionally to prevent sticking. Drain the noodles and rinse with cold water until completely cooled. Set Aside.
Make the Peanut Sauce: While you are cooking the noodles, add the peanut butter, lime juice, soy sauce, garlic, ginger, sugar, sesame oil, and warm water to a small bowl. Whisk well; the mixture should turn clumpy at first, and then smooth out to a lighter, creamy sauce. If needed, add additional water in 1 tablespoon increments until the sauce reaches your desired consistency.
Combine: Add the cooked noodles to a large bowl along with half of the peanut sauce. Use tongs to mix well; this prevents the noodles from sticking. Then, add the cabbage, carrot, cucumber, cilantro, and remaining peanut sauce. Use tongs to mix well, until everything is evenly distributed.
Serve: Top with sesame seeds and serve immediately, or place in the fridge for 15 minutes to serve chilled. Leftovers will keep in the fridge for up to 5 days.
Gluten-Free: If you are gluten-free, look for soba noodles (also known as buckwheat noodles) that are 100% from buckwheat flour and not a wheat & buckwheat blend. Additionally, use a gluten-free soy sauce or tamari.
Nut Allergy: replace the peanut butter with tahini for a similar flavor! If you are only allergic to peanuts you can substitute it with almond butter as well.