Heat 2 Tbsp. oil in a large skillet, preferably nonstick, over medium-high. Add tofu in a single layer and cook, turning over once, until cooked sides are golden brown, about 4 minutes. Transfer to paper towels to drain. Season with kosher salt.
Heat remaining 2 Tbsp. oil in a large pot or high-sided skillet over medium-high. Add onions and a generous pinch of salt and stir to coat. Cook, stirring often, until softened, about 4 minutes. Stir in curry paste and cook, stirring often, until darkened in color, about 2 minutes. Add zucchini, eggplant, and green beans (chickpeas if using) and cook, tossing to coat, until vegetables are softened and starting to brown in spots, 5–7 minutes. Pour in coconut milk and ½ cup water and bring to a simmer.
Add tofu to pot and stir gently to combine. Cook until warmed through, about 3 minutes. Season with more salt if needed.
Divide curry among bowls and add a generous squeeze of lime juice to each. Top with cilantro and peanuts.
