Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Toss the broccoli florets and sliced carrots on the baking sheet with half of the olive oil, half of the sea salt, and half of the black pepper.
Roast the vegetables in the oven for 15-20 minutes until they are tender and slightly caramelized at the edges.
While the vegetables roast, mince the garlic and season the chicken breast on both sides with the remaining sea salt, black pepper, and dried thyme.
Heat the remaining olive oil in a stainless steel or cast-iron skillet over medium-high heat.
Place the chicken in the hot skillet and sear for 5-7 minutes per side, or until the internal temperature reaches 165°F.
In the last minute of cooking, add the minced garlic to the pan and squeeze the juice of the half lemon over the chicken to deglaze the pan.
Let the chicken rest for 3 minutes before slicing and serving alongside the roasted vegetables.