Drain and cut the tofu into 3/4-inch-thick slices. Cut each slice crosswise into 1/2-inchwide sticks (you should have fat, rectangular sticks). Put the tofu on paper towels and set aside. In a small bowl, mix the broth, jalapeño, sesame oil, and sugar.
Set a 12-inch skillet over medium-high heat until hot, about 1 minute. Add 1-1/2 Tbs. of the canola oil and once it's shimmering hot, add the bok choy, cut side down. Sprinkle with 1/2 tsp. of the salt and cook, without touching, until browned, about 2 minutes. Continue to cook, tossing, until the bok choy stems start to soften and wilt, about 2 minutes more. Transfer to a plate.
Add the remaining 1-1/2 Tbs. canola oil and the ginger to the skillet and cook, stirring, until golden, about 1 minute. Add the garlic and let it sizzle for 10 seconds. Add the tofu and shiitakes, sprinkle with the remaining 1/2 tsp. salt, and cook, stirring occasionally, until the mushrooms brown and soften, about 3 minutes.
Return the bok choy to the pan, add the broth mixture, and cook, tossing, until the sauce evenly coats the vegetables and the bok choy is tender, about 2 minutes. Serve immediately.