Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Toss the broccoli florets, sliced red bell pepper, and zucchini with olive oil, sea salt, and black pepper on the prepared baking sheet.
Roast the vegetables for 15-18 minutes until they are tender and show slight caramelized edges.
While the vegetables roast, season the chicken breast with a pinch of salt and sear in a non-stick skillet over medium-high heat for 5-6 minutes per side until fully cooked.
Remove the chicken from the skillet and set aside to rest; in the same skillet, add the minced garlic, grated ginger, and red curry paste, sautéing for 1 minute until fragrant.
Whisk in the full-fat coconut milk and bring the mixture to a gentle simmer for 2-3 minutes until the sauce thickens into a creamy consistency.
Slice the chicken breast into strips and return it to the skillet, tossing thoroughly to coat in the red curry sauce, then finish with a fresh squeeze of lime juice.
Plate the creamy curry chicken alongside the roasted vegetables and serve immediately.