Cut tofu into 6 even pieces widthwise. Line a baking sheet with a double layer of paper towels. Place tofu pieces flat on the paper towels. Place another double layer of paper towels over the tofu, top with another cookie sheet. Place a heavy object such as a cast-iron skillet or books on the top cookie sheet. Set aside.
Cook the pasta according to package directions in salted water. 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 non-stick skillet or wok over medium-high heat. Add tofu cubes and brown well on all sides, tossing or stirring frequently, 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 sesame sauce combination and bring to a simmer. Reduce heat to low, stir in pasta and tofu and toss gently to heat through. Garnish with sesame seeds and serve immediately.