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1
Boil broccolini in a pot of salted water until it's bright green, 2 to 3 minutes. Drain, rinse with cold water, and drain well. Set aside.
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2
Cut tofu into very thin (1/8 in. thick) slices and put in a bowl. Stir together 1 tsp. sugar, 1/4 tsp. pepper, the vinegar, 1 1/2 tbsp. soy sauce, and 2 tsp. sesame oil in a small bowl. Put next to stove along with tofu, duck meat, and garlic.
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3
Slice duck skin thinly and heat, along with fat, in a large wok or frying pan over medium-high heat. Cook fat and skin, stirring 2 to 3 minutes, until most of the fat has melted and skin is crisp. Transfer skin with a slotted spoon to paper towels. Pour off all but about 2 tbsp. fat from pan (if you don't have that much fat, add canola oil to make up the difference).
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4
Add garlic to pan and let sizzle just until fragrant, about 15 seconds. Add tofu and a pinch each of salt and sugar. Cook 30 seconds, then add duck meat and stir-fry 30 seconds to heat through. Add broccolini and stir-fry 2 minutes to heat.
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5
Stir seasoning sauce again, then add to wok. Cook until most of the liquid has been absorbed, about 1 minute. Season with extra salt or soy sauce if you like. Transfer to a plate or shallow bowl and sprinkle with remaining 1 tsp. sesame oil and white pepper to taste. Serve duck cracklings on the side so they stay crisp, for sprinkling on top.
