Prepare vegetables: Dice onion. Cut carrot into bite-sized pieces then into slices about ⅓-inch thick. Cut mushrooms into slices. Grate ginger. Mince or crush garlic into small pieces.
Add oil and butter to skillet over medium heat. Once melted, add diced onion and cook until fragrant and translucent (2-3 minutes). Meanwhile salt shrimp and set aside.
Add minced garlic, grated ginger, and curry powder to heated pan and cook until fragrant (about one minute). Stir in tomato paste and cook another two minutes until darkened slightly.
Add coconut milk, carrots, and mushrooms to pan with a pinch of sea salt and bring to a simmer (about four minutes).
Add shrimp to pan, covering with the sauce and cook until cooked through, stirring occasionally (about 5 minutes). Remove from heat.
Squeeze lime juice over top of curry then stir. Serve over rice and garnish with fresh mint leaves, as desired.