Place chicken breasts on a cutting board and pat dry with paper towels.
In a small bowl, mix salt, black pepper, garlic powder, and paprika.
Season both sides of each chicken breast evenly with the seasoning mixture.
Heat olive oil in a large skillet over medium-high heat.
Add the chicken breasts to the skillet and cook for 6-7 minutes on one side without moving, until golden brown.
Flip the chicken breasts and cook for another 6-7 minutes, or until the internal temperature reaches 165°F (74°C). Remove chicken from skillet and let rest on a plate covered loosely with foil.
While the chicken cooks, place the potatoes in a large pot and cover with cold water. Add a pinch of salt and bring to a boil over high heat.
Reduce heat to medium and simmer potatoes for 15-18 minutes, or until fork-tender.
Drain the potatoes and return them to the pot. Add milk, butter, salt, and pepper, and mash until smooth and creamy. Cover and set aside to keep warm.
In the same skillet used for chicken, add minced garlic, baby carrots, and green beans.
Sauté vegetables over medium heat for 5-7 minutes, stirring occasionally, until tender-crisp.
Serve each chicken breast with a portion of garlic mashed potatoes and sautéed vegetables.