Preheat the oven to 375°F (190°C).
In a small bowl, mix together the kosher salt, black pepper, dried thyme, and dried rosemary.
Pat the turkey breast dry with paper towels. Rub 2 tablespoons of olive oil evenly over the turkey breast, then sprinkle the seasoning mixture all over the turkey, pressing gently to adhere.
Place the quartered onion, carrots, and celery in the bottom of a roasting pan. Drizzle with the remaining 1 tablespoon olive oil and toss to coat.
Set the seasoned turkey breast on top of the vegetables in the roasting pan. Spread the minced garlic over the turkey breast.
Roast the turkey breast in the preheated oven for about 1 hour and 15 minutes, or until an instant-read thermometer inserted into the thickest part of the breast reads 165°F (74°C).
Remove the turkey breast from the oven and transfer it to a cutting board. Tent loosely with foil and let rest for 15 minutes.
While the turkey rests, place the roasting pan with vegetables and pan juices on the stovetop over medium heat.
Add the chicken broth to the pan and bring to a simmer, scraping the bottom of the pan to loosen browned bits.
In a small bowl, whisk together the all-purpose flour with 2 tablespoons of water until smooth. Slowly whisk this mixture into the simmering pan juices and cook for 2 to 3 minutes until the gravy thickens.
Slice the turkey breast and serve with the roasted vegetables and pan gravy.