Put the potatoes in a medium saucepan, add water to cover by about 3/4 inch, and add 1 Tbs. salt. Bring to a boil over high heat, reduce the heat to maintain a simmer, and cook until the potatoes are tender but not falling apart, about 5 minutes. Drain the potatoes, transfer to a plate, and set aside.
Heat the oil in a 10-inch straight-sided sauté pan over medium-high heat. Add the onion and 1/2 tsp. salt and cook, stirring occasionally until soft, 5 to 7 minutes. Add the pork and continue to cook until the pork is warm, about 3 minutes. Add the garlic and cook, stirring, until the raw garlic aroma subsides, about 1 minute. Add the potatoes, toss gently to combine, and continue to cook, stirring, until heated through, 1 to 3 minutes more. Season to taste with salt. If the hash is a little dry, add a drizzle of olive oil. Keep warm.
Fill a medium saucepan with 3 inches of water. Add the vinegar and a pinch of salt, and bring the water to a simmer. Crack the eggs one at a time into a small bowl or teacup and then gently slide each egg into the water. Poach the eggs, gently turning once or twice until the whites are completely opaque but the yolks are still soft, 3 to 4 minutes. Using a slotted spoon, remove the eggs from the water and gently blot dry with a towel.
Evenly distribute the hash among 4 plates. Prop a poached egg and a few slices of avocado next to each portion. Sprinkle the egg and avocado with salt. Sprinkle the cilantro and piment d’Espelette (if using) over the hash, and serve immediately.