Once the chicken is done marinating, preheat your Blackstone griddle to medium-high heat and coat the surface with a thin layer of vegetable oil or avocado oil.
Spread the marinated chicken out onto the griddle. Reserve the marinade. Let it cook, flipping occasionally with your griddle spatulas, until it is beautifully browned and cooked completely through. Remove the chicken from the griddle and place it in a bowl.
Batch cook your vegetables. This means that you will want to cook your hardier vegetables first and then add in the softer vegetables when the other is about halfway done cooking. Therefore, cook the broccoli, onions, and carrots first, cooking until slightly tender (1-2 minutes). Then add in the red peppers (about 1-2 minutes). When those are slightly tender, add in the cabbage and shiitake mushrooms (1-2 minutes). Stir-fry them constantly until they are tender yet crisp.
While vegetables are cooking, in another zone, add your 32 oz of yakisoba noodles directly onto the griddle next to the vegetables. Toss them frequently for a few minutes until they are warmed through and begin to get a slight crisp on the edges.
Move the vegetables, and noodles aside to create a safe zone to heat your marinade. Carefully, add your reserved marinade to the grill and bring it to a boil for 2 minutes to make it safe for eating. Alternatively, you can boil your marinade on the stove ahead of time or make twice as much marinade, but only use half of it for the raw chicken, reserving the other half for cooking.
Bring the cooked chicken, stir-fried vegetables, yakisoba noodles, and marinade all together into one big pile on the griddle surface. Toss thoroughly so all the savory flavors from the chicken marinade coat the noodles and veggies evenly.
Remove the yakisoba from the griddle, pile it high onto a serving platter, and top with the sliced scallions. Serve immediately while it's hot.