Cook the noodles
Bring a pot of salted water to a boil and cook the noodles according to package directions (most need about 3–4 minutes). Drain and set aside. Toss them with a little oil if they might stick.
Sauté the broccoli (or mushroom)
Heat 1 Tbsp oil in a large skillet over medium-high heat. Add broccoli and sauté 5–6 minutes until crisp-tender. Transfer broccoli to a bowl and lower the heat.
Build the lemon-garlic sauce
Add vegan butter and the remaining 1 Tbsp oil to the skillet. Stir in two-thirds of the scallions, garlic, ginger, and chili flakes. Sauté ~3 minutes until fragrant. Pour in the soy sauce and let the mixture bubble for a moment.
Finish the bowl
Add the cooked noodles, broccoli, edamame, and toasted sesame seeds. Use tongs to toss everything well so the noodles coat in the lemon-garlic scallion sauce. Taste and add a squeeze of lemon or more soy if you want extra zip.
Serve & garnish
Divide the noodles between bowls. Sprinkle with the remaining scallions, extra sesame seeds, and a drizzle of chili oil if you like heat. Serve immediately.