Trim ends from zucchini and cut into quarters. Trim out seeds if zucchini are really big. Cut into 1 ½-inch pieces and add to a bowl. Toss thoroughly with 2 tablespoons kosher salt and let sit for 15 to 20 minutes, tossing halfway through.
Transfer zucchini to a strainer and rinse off salt very thoroughly. Let drain well before transferring to a bowl.
Set an oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with foil.
Toss zucchini with 2 tablespoons olive oil, toss, and spread out in a single layer on the prepared baking sheet, making sure zucchini pieces touch each other.
Broil on high heat until zucchini start to brown and are lightly charred, 5 to 6 minutes. Remove pan and turn zucchini pieces over. Return and broil until zucchini are tender but not mushy, and nicely browned, 5 to 6 minutes longer.
Transfer zucchini to a strainer and let drain until cooled to room temperature, about 45 minutes.
Combine drained zucchini, remaining 2 tablespoons olive oil, tahini, garlic, lemon juice, basil, ½ teaspoon salt, cumin, black pepper, and cayenne in a blender. Blend until smooth, and taste for seasoning. You can also use an immersion blender.
For best flavor, cover and chill the hummus before serving.
