Preheat the oven to 325 degrees F.
Add the Neelys' BBQ Sauce, garlic, onions and diced tomatoes to a food processor and blend until smooth.
Sprinkle the brisket on both sides with salt and pepper. Heat a large Dutch oven over medium-high heat. Add the oil and once hot, add the brisket and brown, 5 minutes per side. Transfer the brisket to a plate. Pour the beer into the Dutch oven, scraping up any browned bits on the bottom of the pan. Stir in the chicken broth and pureed tomato mixture. Add the brisket back into the pot and bring to a simmer. Cover with a lid and transfer to the oven until the brisket is incredibly tender and the meat is beginning to fall apart, about 3 hours. Shred the meat in the pot with tongs and place the mixture into a 2-quart casserole dish. Add the peas in a layer on top of the brisket.
Meanwhile, add the potatoes to a large pot of cold salted water. Bring up to a boil, reduce to a simmer and cook until tender. Drain in a colander, then mash in a large bowl. Stir in milk and butter, and season with salt and pepper.
Spread the potatoes evenly on top of the meat and pea layer. Use a spoon to create some texture on the layer of mashed potatoes. Bake until golden and brown, 30 to 35 minutes.
In a medium saucepan, combine the ketchup, 1 cup water, vinegar, brown sugar, granulated sugar, mustard, onion powder, pepper, lemon juice and Worcestershire sauce. Bring the mixture to a boil, and then reduce the heat to a simmer. Cook uncovered, stirring frequently, 1 hour 15 minutes.