Heat the canola oil in a large skillet over medium-high heat. Add the mushrooms and cook, tossing occasionally, until soft, 3 to 4 minutes.
Add the garlic and ginger to the skillet and cook until fragrant, about 1 minute. Add the watercress and ½ teaspoon salt and cook, tossing, until tender, 2 to 3 minutes more. Remove from heat, add the sesame oil, and toss to combine.