Combine the water, brown sugar, and 3/4 cup kosher salt in a 2-gallon or larger stockpot or other nonreactive container, and whisk until the sugar and salt have dissolved. Submerge the turkey breast in the brine and refrigerate it for 8 hours.

Remove the turkey from the brine, rinse it, and pat it dry with paper towels. Refrigerate, covered, until ready to cook. Preheat a grill to medium-high.

In a medium bowl, combine the onions, celery, garlic, oregano bundle, 1 teaspoon of the Rib Rub, and the 2 tablespoons olive oil. Add 1 cup of the tomatoes, and stir together. Pour the vegetables into the outer well of the vertical roaster. Fill the inner well with beer, and pour the remaining beer over the vegetables.

Brush the remaining 1/4 cup olive oil over the turkey breast. Sprinkle the remaining 2 teaspoons Rib Rub over the outside of the turkey, and season it lightly with kosher salt and black pepper.

Position the turkey breast over the inner well of the roaster so that it sits securely upright. Place the roaster on the grill, close the lid, and cook, basting every 20 minutes with the accumulated pan juices, until the turkey is golden brown and an instant-read thermometer inserted into the deepest portion of the breast registers 165 degrees, usually about 1 hour. (If the skin browns too quickly during cooking, cover the turkey with foil. If the liquid in the well of the roaster evaporates during cooking and before the turkey is done, add more chicken broth as necessary.)

Remove the roaster from the grill, and set the turkey on a cutting board to rest for 10 minutes before carving. Transfer the vegetables and pan juices from the inner and outer wells of the roaster to a blender, and set aside.

While the turkey is resting, make the gravy: In a small saucepan, whisk together the vinegar, remaining 1 cup canned tomatoes, dark brown sugar, molasses, salt, oregano, and crushed red pepper. Bring to a boil. Then reduce the heat to a simmer and cook until the flavors blend and the sauce thickens slightly, about 15 minutes.

Add the barbecue sauce to the vegetables in the blender, and blend until smooth. (Please be cautious while blending the hot sauce, as the steam may cause the top of the blender to open. Either hold the lid down with a towel or wait for the sauce to cool slightly before blending.) Transfer the gravy to a bowl or sauceboat, and keep it warm until ready to serve.

Carve the turkey breast into thin slices, and serve with the BBQ gravy.