In a small bowl, stir together soy sauce, hoisin sauce, chili crunch, dark sesame oil, brown sugar, lime juice, and ginger until sugar is dissolved.
In a large skillet, heat 1 tablespoon olive oil over medium-high heat. Add onion; cook until softened, about 3 minutes. Add garlic; cook until fragrant, about 30 seconds. Add beef, breaking up meat with a wooden spoon, until browned, about 5 minutes.
Transfer beef mixture to a large bowl. Add half of soy sauce mixture, tossing to coat.
In same skillet, heat 1 tablespoon olive oil over medium-high heat. Add half of cabbage and cook until browned, 2 to 3 minutes. Repeat with remaining cabbage and 1 tablespoon oil. Add cabbage mixture to beef mixture.
In same skillet, heat remaining 1 tablespoon olive oil over medium-high heat. Add carrot, green onion, broccoli, and sugar snap peas, stirring often, until crisp-tender, about 3 minutes. Add to beef mixture. Add remaining soy sauce mixture, stirring to coat. Serve warm with lime wedges. Garnish with peanuts, if desired.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/cabbage-stir-fry/