Start by draining the tofu. Cut the tofu into 6 even slabs widthwise.--Line a sheet pan with a clean kitchen towel or double layer of paper towels. Place tofu slabs flat on the paper towels.--Place another clean kitchen towel on top or another double layer of paper towels.--Place another baking sheet over the tofu.--Place a heavy item such as a cast-iron skillet or several heavy books on the top cookie sheet. Alternatively, use a tofu press. Set aside.
Bring a pot of salted water to a boil. Cook the pasta according to the package directions. Drain in a colander and toss with 1 tablespoon sesame oil.
Whisk together vegetable broth, tahini, soy sauce, honey, rice vinegar, chili garlic sauce, ginger and garlic. Set aside.
Cut tofu into cubes. Heat 1 tablespoon oil in a large skillet or wok over medium-high heat.
Add tofu cubes and brown well on all sides, tossing or stirring frequently, approximately 5-7 minutes. Transfer to a plate or into the colander with the drained pasta.
Refresh oil if needed. Add broccoli slaw to skillet. Cook 1-2 minutes, stirring often until beginning to soften.
Add scallion and cook 1 minute more.
Add sauce combination and bring to a simmer. Reduce heat to low.
Stir in pasta and tofu and toss to gently heat through.
Garnish with sesame seeds if desired and serve immediately.