Preheat your oven to 425°F.
Peel and cut the carrot and parsnip into uniform sticks or rounds for even roasting.
Toss the vegetables in a bowl with olive oil, salt, and pepper until evenly coated.
Spread the vegetables on a baking sheet in a single layer and roast in the oven for about 20-25 minutes until tender and slightly caramelized.
Season the chicken breast on both sides with salt and pepper.
Heat a skillet over medium-high heat and add a small drizzle of olive oil.
Place the chicken breast in the skillet and sear for 3-4 minutes on each side until a golden crust forms.
Reduce the heat to medium-low and add butter along with minced garlic (from the cloves). Allow the butter to melt and the garlic to infuse the chicken for an additional 2-3 minutes, spooning the garlic butter over the chicken as it cooks.
Once the chicken is fully cooked (internal temperature reaches 165°F), remove it from the skillet.
Plate the chicken alongside the roasted root vegetables, drizzling any remaining garlic butter from the skillet over the top, and serve immediately.