Preheat your oven to 200°C (180°C fan). Slice the carrots into thin sticks and cut the broccoli into florets. Toss the vegetables in 1 tbsp of olive oil, salt, and pepper. Spread them evenly on a baking tray.
Roast the vegetables in the preheated oven for about 20-25 minutes until tender and slightly caramelised, turning halfway through.
While the vegetables are roasting, mince the garlic cloves. In a small bowl, mix the minced garlic, honey, soy sauce, lemon juice, and thyme to create the sauce.
Heat 2 tbsp of olive oil in a large frying pan over medium-high heat. Season the chicken breasts with salt and pepper, then sear them in the pan for about 3-4 minutes on each side until golden brown.
Reduce the heat to medium and pour the honey garlic sauce over the chicken. Cook for an additional 5-7 minutes, turning the chicken occasionally, until the sauce thickens and the chicken is cooked through.
Serve the chicken breasts drizzled with the remaining sauce, alongside the roasted vegetables. Garnish with fresh thyme if desired.
