Place the diced red potatoes in a medium pot, cover with cold water and 1/2 teaspoon salt. Bring to a simmer and cook for 6–8 minutes until just tender but not falling apart. Drain well and let steam-dry for 2 minutes.

Sauté onion and start hash

In a large skillet over medium-high heat, add 2 tablespoons vegetable oil and 1 tablespoon butter. When the fat is hot and shimmering, add the chopped onion and a pinch of salt. Sauté, stirring occasionally, for 5–7 minutes until the onion is soft and beginning to caramelize.

Add potatoes and spices

Add the par-cooked diced potatoes to the skillet. Spread into a single layer and let cook undisturbed for 2–3 minutes to get a light crust. Stir and continue to cook another 4–6 minutes, pressing occasionally, until potatoes are golden. Stir in the smoked paprika, ground cumin, 1/2 tsp black pepper, and 1 teaspoon salt; cook 1 minute to bloom the spices.

Finish hash with brisket and tomato

Add the shredded brisket and minced garlic to the skillet, tossing to combine and heat the meat through, about 3–4 minutes. Add the diced tomato and cook 1–2 minutes more until tomatoes are slightly softened but not mushy. Taste and adjust seasoning. Stir in chopped parsley or cilantro if using. Keep the hash warm while you prepare the eggs and aioli.

Spicy Aioli

In a small bowl, whisk together 1/2 cup mayonnaise, 1 tablespoon sriracha, 1 teaspoon lemon juice, 1/4 teaspoon smoked paprika, 1/4 teaspoon garlic powder and 1/8 teaspoon salt until smooth. Taste and adjust heat or acidity as desired. Chill or leave at room temperature until assembly.

Eggs & Assembly

Cook the eggs

Option A — Scrambled: In a bowl, crack the 4 eggs, add 2 tablespoons milk or water and a pinch of salt and pepper; beat until blended. Heat a nonstick skillet over medium-low and add 1 teaspoon butter. Pour eggs in and cook gently, stirring, until soft curds form but still slightly moist. Option B — Fried: Heat 1 teaspoon butter or oil in a skillet over medium-high and fry eggs to desired doneness (sunny-side up or over-easy).

Warm tortillas

Warm the flour tortillas one at a time in a dry skillet over medium heat about 20–30 seconds per side until soft and pliable, or wrap in foil and heat in a 300°F (150°C) oven for 8–10 minutes.

Assemble the wrap

Lay a warm tortilla on a flat surface. Spread about 1 to 1 1/2 tablespoons of spicy aioli in a line down the center. Spoon 1/2 cup brisket hash down the center of the tortilla. Top the hash with a quarter of the eggs (about 1 egg's worth) and 1/4 cup shredded cheese if using. Drizzle another 1 teaspoon of aioli on top. Fold the short sides in, then roll tightly to form a wrap. Repeat with remaining tortillas and components.

Optional crisp and serve

To crisp the wraps, heat a skillet over medium and lightly butter or oil it. Place each wrap seam-side down and cook 1–2 minutes per side until golden and slightly crisp. Slice in half on the diagonal and garnish with cilantro or parsley. Serve immediately with extra aioli on the side.