Heat 2 tablespoons vegetable oil in a large cast-iron skillet over medium-high heat. Add the potatoes and cook, undisturbed, until they start to color, about 5 minutes. Stir and continue cooking until golden, about 3 more minutes. Add the red onion and jalapeno; season with salt and cook, stirring, 3 minutes. Stir in the brisket and cook until heated through. Add 3/4 cup brisket sauce and cook, stirring, until absorbed, about 3 minutes.
Stir in the Swiss chard until just wilted, about 2 minutes. Season with salt, then arrange the sliced cheese on top. Cook until the cheese begins to melt, about 1 more minute.
Meanwhile, heat the remaining 1 tablespoon vegetable oil in a large nonstick skillet over medium-high heat. Add the eggs and season with salt. Cook until the whites are set, about 3 minutes.
Divide the hash among plates; top each with a fried egg. Heat the remaining 1/4 cup brisket sauce in the empty skillet. Drizzle on the hash. Serve with the avocado.
Slow-Cooker Barbecue Brisket
Combine the brown sugar, chile powder, cumin, celery salt, garlic, and salt and pepper to taste in a small bowl. Rub all over the brisket, then transfer to a 5-to-6-quart slow cooker. Combine 3/4 cup ketchup, the vinegar and Worcestershire sauce in another small bowl. Pour over the brisket along with 3/4 cup water. Cover and cook on low, 8 hours.
Remove the brisket to a cutting board and let rest 10 minutes. Meanwhile, skim off the excess fat from the sauce; stir in the remaining 1/2 cup ketchup. Reserve one-third of the brisket (about 12 ounces) and 1 cup of the brisket sauce for Southwestern Brisket Hash. Slice the remaining brisket and divide among plates. Top with some of the sauce and serve with potato salad and cornbread.
Per serving: Calories 453; Fat 12 g (Saturated 5 g); Cholesterol 115 mg; Sodium 676 mg; Carbohydrate 16 g; Fiber 0 g; Protein 67 g