In a large serving bowl, add the cucumber and carrots. Set aside.
In a separate medium mixing bowl, whisk together all of the sauce ingredients: vegetable oil, rice vinegar, sesame oil, soy sauce, sugar, sesame seeds, salt, and pepper. Taste, and add more salt and pepper if necessary.
Pour the sauce over the cucumber and carrots, then toss with a wooden spoon or tongs to fully coat the vegetables with the sauce. Serve immediately.
Notes
Storage: Store in an airtight container in the refrigerator for up to 4-5 days. For deeper flavor: add a splash of hoisin sauce or oyster sauce to the sauce mixture.