Heat a large heavy-duty skillet over medium-high heat for 1–2 minutes and add 1 teaspoon oil.
Season the chicken breasts with salt and pepper and cook in the hot pan until golden and cooked through, about 5–6 minutes per side depending on thickness.
Remove chicken from the pan and let cool 5 minutes, then chop into chunks or slices.
While the chicken cooks, thinly slice the cabbage, red pepper, and carrots into julienne-style strips; slice the cucumber if using and chop the cilantro.
In a medium bowl, whisk together the peanut butter, soy sauce or tamari, sesame or olive oil, rice vinegar, minced ginger, minced garlic, sriracha (if using), lime juice, and water until smooth and loosely thinned.
To assemble each tortilla, lay it flat and add about one-third of the slaw, cilantro, and cooked chicken, sprinkle with crushed peanuts, and drizzle about 1 tablespoon of peanut sauce.
Fold each tortilla tightly like a burrito and slice each into 4 rolls; repeat with the remaining tortillas to make 12 rolls total.
Place three rolls in each meal-prep container, add about 1/2 cup grapes to each, and divide the remaining peanut sauce into four 2 oz portion cups; cover and refrigerate.
Reheat briefly in the microwave or enjoy cold as desired.