Heat the coconut oil in a large pot over medium heat. Add the Thai red curry paste, minced garlic, and grated ginger, then sauté for 1 to 2 minutes until highly fragrant and sizzling.

Pour in the vegetable broth and coconut milk, stirring well to fully dissolve the curry paste. Bring the liquid to a gentle boil, then reduce the heat to low to maintain a steady simmer.

Add the sliced shiitake mushrooms, red bell pepper, and broccoli florets to the simmering broth. Cook for about 5 to 7 minutes, or until the vegetables are tender-crisp and vibrant in color.

Stir in the soy sauce and lime juice, mixing well to balance the savory and tangy flavors. Taste the broth and adjust the seasoning with extra soy sauce or a pinch of salt if desired.

Ladle the hot broth and vegetables into bowls, and garnish generously with fresh cilantro and lime wedges. Serve immediately alongside steamed rice or cooked rice noodles for a complete, comforting meal.