Stage 1 - Noodles (Can Do Night Before)
Cook lo mein noodles according to package directions until al dente firm with some resistance when bitten, not fully soft.
Drain and immediately toss with the 2 tablespoons of sesame oil in a large bowl. Toss thoroughly every noodle strand should be coated. Cover the bowl with plastic wrap or transfer to an airtight container and refrigerate for 1 hour minimum (up to overnight if making ahead).
Stage 2 - Vegetables (During Chill Period)
Cut the scallions, bell pepper, carrot, and cucumber into thin matchsticks as described above. Set aside a few pieces of each vegetable for garnish if desired. Store cut vegetables covered until assembly.
Stage 3 - Make the Sauce
In a medium bowl, whisk together the soy sauce, peanut butter, tahini, rice vinegar, sesame oil, brown sugar, chili garlic sauce, grated ginger, and grated garlic until completely smooth.
The sauce should be thick but pourable similar to a thin BBQ sauce consistency. If it's too thick to pour easily, add 1-2 tablespoons of warm water and whisk again.
Taste before adding to noodles- The sauce should taste intensely flavored salty, nutty, slightly sweet, and noticeably spicy. It will mellow slightly when distributed across 12 ounces of noodles and the vegetables.
Stage 4 - Assembly
Remove the chilled noodles from the refrigerator. Add the cut vegetables to the noodle bowl. Pour the sauce over everything.
Toss thoroughly - use tongs or two forks to lift and fold the noodles with the sauce and vegetables rather than stirring in circles. Circular stirring tangles the noodles; lifting and folding distributes the sauce more evenly.
Arrange reserved vegetable pieces on top as garnish. Sprinkle with sesame seeds.
Serve immediately - this dish is at its best texture immediately after tossing, while the vegetables are still at peak crispness.