Add the diced potatoes to a pot of cold salted water. Bring to a boil and cook for 3 minutes. Immediately strain. Lay the potatoes over paper towels and carefully pat dry.
In a large skillet, heat the olive oil over medium-high heat. Add the par-boiled potatoes and season with salt and pepper. Cook for 10-15 minutes, stirring as needed. Add the onion, red and green pepper, and jalapeno (if using). Cook for another 15-20 minutes, stirring as needed, until the potatoes are golden and crispy (you may need to lower your heat to medium - so keep an eye on things).
Add the minced garlic and cook for one minute longer. Remove from heat.
Whisk the mayo with the minced chipotle pepper and desired amount of adobo sauce for your heat preference. In a clean bowl, toss the cooked hash in the chipotle cream to coat lightly. Fold in the arugula and cherry tomatoes.
Prep the bowls with the hash and arugula mix, dividing equally into each bowl. Add the chorizo on top.
Meanwhile, poach the eggs by bringing a saucepan of water to a gentle boil. Add the white wine vinegar. Crack each egg into a small bowl. Gently drop each egg into the water and cook for 3 minutes. Carefully remove with a slotted spoon, gingerly shaking off any excess water.
Place a poached egg over each bowl and garnish with sliced avocado and freshly minced cilantro. Serve immediately.