Heat oil in a large skillet or wok over medium-high heat; cook and stir scallions, 1 to 2 minutes. Add garlic and ginger; cook and stir until fragrant, 1 to 2 minutes. Add pork; cook and stir until browned and crumbly, 5 to 7 minutes.

Mix hoisin sauce, beer, ground bean sauce, and sugar into pork mixture. Reduce heat to medium and simmer until sauce is thickened, about 5 minutes. Add bok choy and stir to incorporate. Reduce heat to medium-low and cook until bok choy is tender, about 5 minutes more.

Bring a large pot of lightly salted water to a boil. Cook noodles in the boiling water until tender yet firm to the bite, 1 to 3 minutes; drain and transfer to a bowl.

Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add mung beans, cover, and steam until tender, 2 to 4 minutes.

Serve sauce over noodles and top with cucumber, carrots, and bean sprouts.