Preheat your oven to 375°F and season the chicken with salt and pepper.
Melt 2 tablespoons of butter in a large ovenproof skillet over medium heat. Add the chicken and sear until golden brown, about 10-12 minutes. Transfer to a plate.
Reduce heat to medium-low, add remaining butter, green beans, shallot, garlic, and Italian seasoning. Cook for about 7 minutes until green beans are crisp-tender.
Remove from heat, zest the lemon into the pan, and squeeze in the lemon juice. Stir in coconut milk.
Return the chicken to the skillet, nestling among the green beans and sauce. Bake for 15-25 minutes until the chicken reaches 165°F.
Remove from oven, garnish with fresh herbs, and serve with lemon wedges.
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Notes
Store leftovers in an airtight container in the refrigerator for up to 3 days. Reheat gently on the stove or microwave.