Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Toss the broccoli florets with the olive oil, half of the sea salt, and half of the black pepper directly on the baking sheet.
Roast the broccoli for 15-20 minutes until the edges are crispy and charred.
While the broccoli is roasting, season the chicken breast with the remaining sea salt and black pepper.
Heat a large skillet over medium-high heat and sear the chicken for 5-7 minutes per side until golden and cooked through.
Remove the chicken from the skillet and set it aside on a plate, then reduce the heat to medium.
Add the minced garlic, grated ginger, and ground turmeric to the skillet and sauté for 60 seconds until fragrant.
Pour in the full-fat coconut milk and lime juice, using a spatula to scrape up any flavorful browned bits from the pan.
Simmer the sauce for 2-3 minutes until it begins to thicken, then return the chicken to the pan to coat it thoroughly.
Serve the creamy chicken immediately alongside the tender roasted broccoli.