Cook rice as directed on package.
Mince garlic. Trim and discard bottom root ends from bok choy; thinly slice stalks and leaves crosswise. Halve, peel, and thinly slice shallot.
Heat a large pan over medium-high heat. Add pork and shallot and cook, stirring, until softened and pork has browned.
Add garlic; cook until fragrant and pork has cooked through, 1 minute more. Add salt and pepper to taste.
Meanwhile, stir together water, juice from half the lime, fish sauce, and sriracha. Set aside.
Add bok choy, matchstick carrots, and soy sauce to the pan with pork. Cook, tossing, until bok choy and carrots are tender, about 3 minutes. Stir in the sauce and basil; heat through.
Serve pork over rice with pears on the side.