Bring a large pot of salted water to a boil. Add the noodles and cook until tender. Drain well and set aside.

Whisk the dark brown sugar, molasses, and soy sauce in a small bowl until the sugar dissolves. In a separate small bowl, mash the minced shallots, garlic, and sambal oelek into a rough paste.

Pat the tofu very dry with paper towels and toss with salt, pepper, and cornstarch until the cubes are evenly coated.

Heat the vegetable oil in a large nonstick skillet over medium-high heat until shimmering. Add the sliced shallot rings and cook, stirring frequently, until they are golden brown and crisp, 3 to 5 minutes. Transfer the shallots to a paper towel-lined plate using a slotted spoon, keeping the oil in the pan.

Increase the heat to high. Add the tofu to the hot oil and cook until browned and crisp on all sides, about 8 minutes. Transfer the tofu to a plate.

Add the bok choy stalks to the skillet and cook until they begin to soften and take on a little color, about 2 minutes.

Stir in the shallot-garlic-sambal paste and cook until fragrant, about 30 seconds. Add the cooked noodles, the soy sauce mixture, the bok choy greens, and the browned tofu. Toss constantly until the sauce thickens and glazes the noodles completely, about 2 minutes.

Serve immediately, topped with the crispy fried shallots and scallions, with lime wedges on the side to balance the sweetness.