Peel, then mince or grate garlic. Trim, then halve snow peas. Add vegetarian oyster sauce, sweet chilli sauce, gochujang and sesame oil in a medium bowl. Stir to combine.
Add linguine to the boiling water. Cook uncovered, stirring occasionally, until tender, 10-12 min. Reserve ¼ cup (½ cup) pasta water, then drain and return linguine to the same pot, off heat.
While linguine cooks, heat a large non-stick pan over medium-high heat. When hot, add ½ tbsp (1 tbsp) oil, carrots, and snow peas. Season with salt and pepper. Cook, stirring often, until tender-crisp, 2-4 min. Transfer veggies to a plate.
Return the same pan to medium-high. When hot, add ½ tbsp (1 tbsp) oil, then beef and garlic. Season with salt and pepper. Cook, breaking up beef into smaller pieces, until no pink remains, 4-5 min.** Add veggies and sauce mixture. Cook, stirring often, until warmed through, 1-2 min.
Transfer saucy meat and veggie mixture to the pot with linguine. Add spinach. Season with salt and pepper, to taste. Stir until wilted, 1 min. (TIP: For a lighter sauce consistency, add reserved pasta water, 1-2 tbsp at a time, if desired.) Divide noodles between bowls. Sprinkle sesame seeds over top.
If you've opted to get beef, reduce oil to ½ tbsp (1 tbsp), then add beef to the pan. Cook beef in the same way the recipe instructs you to cook the turkey. [Remove and discard excess fat, if desired.]