Heat 1 Tbsp. of the oil in a large high-sided skillet over medium heat. Cook onion 5 minutes, until softened. Add garlic, ginger, and curry paste; cook 1 to 2 minutes, stirring often, until fragrant. Add remaining 1 Tbsp oil, zucchini, squash, carrots, and bell pepper; cook 5 to 6 minutes, until vegetables develop some color. Season with salt and pepper.
Add coconut milk, broth, nut butter, and corn; bring mixture to a boil. Reduce to a simmer, and cook 15 minutes, uncovered, until vegetables soften and broth slightly thickens.
Meanwhile, prepare mango salad by combining mango, herbs, peanuts, lime juice, and fish sauce in a small bowl; gently toss.
Serve curry over rice and top with mango salad.