Heat vegetable oil in a large pan over medium heat.
Add sliced shallots and minced garlic; sauté until fragrant and translucent, about 2-3 minutes.
Stir in red Thai curry paste and cook for 1 minute to release the aromas.
Pour in the coconut milk and bring to a gentle simmer.
Add fish sauce, palm sugar, and torn kaffir lime leaves; stir to combine.
Add sliced red bell pepper and green beans; simmer for 5 minutes until vegetables are tender-crisp.
Gently place salmon pieces into the curry sauce, cover, and simmer for 6-8 minutes until salmon is cooked through and tender.
Remove from heat; stir in lime juice and fresh Thai basil leaves.
Serve salmon pieces partially submerged in curry sauce in a shallow white bowl.
Garnish with Thai basil leaves and red chili slices; serve with a lime wedge on the side.