Put the sesame seeds in a large skillet over medium-low heat and cook, shaking the pan frequently, until fragrant, about 5 minutes. Put the seeds, black beans, lemon juice, tahini, sugar, garlic, and ¾ teaspoon salt in a blender or food processor along with 1 cup black-bean cooking liquid or water. Process until smooth, and set aside (or store in an airtight container in the refrigerator for up to several days).
Put at least 2 inches of the canola or safflower oil in a large, deep pot over medium-high heat. Combine the flour, baking powder, and 1 teaspoon salt in a large bowl. Add 1¾ cup water and whisk well to combine, then whisk in the sesame oil and balsamic vinegar.
Add a few drops of the tempura batter to the oil to test whether it’s hot enough; the batter should immediately sizzle vigorously. Working in batches, dip the broccoli florets in the tempura batter, let excess batter drip off them, and then transfer them to the oil. Cook, turning once, until deep golden brown, about 1 minute. Transfer the florets to paper towels to drain, and season with salt. Serve hot, dipped in the black-bean hummus.
