In a large skillet or saucepan, heat the vegetable oil over medium heat. Add the diced onion and sauté until translucent, about 3-4 minutes.
Stir in the minced garlic and grated ginger, cooking for an additional 1-2 minutes until fragrant.
Add the sliced red bell pepper and broccoli florets to the skillet. Cook for about 5 minutes, stirring occasionally, until the vegetables are tender-crisp.
Pour in the coconut milk, peanut butter, soy sauce, brown sugar, red curry paste, and vegetable broth. Stir well to combine all ingredients.
Bring the mixture to a gentle simmer and let it cook for 10-15 minutes, stirring occasionally, until the sauce thickens slightly.
Remove from heat and stir in the lime juice. Season with salt and pepper to taste.
Serve the curry over cooked rice or quinoa, garnished with fresh cilantro.