Prep and Broil the Tofu: Preheat your broiler. Lightly coat the unheated rack of a broiler pan with cooking spray.
Cut the tofu block crosswise into 6 slices and pat them very dry with paper towels.
Arrange the slices in a single layer on the prepared rack and brush the tops with 3 tablespoons (45 ml / 1.5 fl oz) of the hoisin sauce. Broil 4 to 6 inches from the heat for 8 to 10 minutes, or until the hoisin is bubbly and caramelized.
Build the Broth and Cook Noodles: Meanwhile, in a 4- to 6-quart Dutch oven or large pot, combine the vegetable broth, minced roasted garlic, and the remaining hoisin sauce.
Bring the mixture to a rolling boil.
Add the dried noodles and cook according to package directions.
Wilt Spinach and Serve: During the last 2 minutes of the noodle cooking time, stir in the fresh baby spinach until it wilts. To serve, divide the noodle mixture among large, deep soup bowls.
Cut the broiled tofu into cubes or strips and place it on top of the noodles.