Preheat oven to 400°F. Cut off the ends of the onions; peel and cut each of the onions into 3, 1/2-inch thick slices. In a roasting pan, make two rows of three slices to form an onion "rack" for the turkey to sit on.
Pat the turkey breast dry with paper towels. Gently work your fingers under the skin of the breast, separating it from the meat (leave skin attached on 1 side). Spread the herbs under the skin of the breast. Set the turkey on the onion "rack" and lightly coat the skin of the breast with olive oil; season with 1/8 teaspoon salt and pepper.
Pour the water into the bottom of the pan. Place the pan in the oven and roast, uncovered, for 60 to 70 minutes or until an instant-read thermometer inserted into the thickest part of the breast registers 165°F to 170°F. Check the turkey after 20 minutes; add 2 to 3 tablespoons additional water to pan if liquid evaporates.
Meanwhile, melt the butter in a small saucepan over medium heat. Add the flour and whisk well until smooth; set aside to cool.
When turkey is done, transfer it from the pan to a cutting board; cover and let rest. Place the roasting pan on the stovetop over medium-high heat. Add the broth and bring to boiling. Reduce heat and cook for 8 minutes, stirring constantly with a wooden spoon to separate onions and to scrape up any browned bits. Add flour mixture and cook and stir until thickened; cook and stir 1 minute more. Season to taste with additional salt. Serve gravy with turkey.