Before starting, preheat the oven to 425°F and wash and dry all produce. Cut potatoes into 1/2-inch pieces. Toss potatoes and 1/2 tbsp oil (dbl for 4 ppl), on a parchment-lined baking sheet. Season with salt and pepper. Roast in middle of oven, flipping halfway through cooking, until golden-brown, 18-20 min.

While potatoes roast, core, then cut pepper into 1/2-inch pieces. Finely chop parsley. Thinly slice green onions. Halve tomatoes. Peel, then mince or grate garlic. Stir together mayo, half the parsley and 1/4 tsp garlic (dbl for 4 ppl), in a small bowl. Set aside.

Heat a large non-stick pan over medium heat. When hot, add 1/2 tbsp oil (dbl for 4 ppl), then onions. Cook, stirring often, until slightly softened, 2-3 min. Add vinegar and 1 tsp sugar (dbl for 4 ppl). Season with salt. Cook, stirring occasionally, until dark golden-brown, 7-8 min. Remove pan from heat. Transfer onions to another small bowl and set aside. Carefully wipe pan clean.

Heat the same pan over medium-high heat. When hot, add 1/2 tbsp oil (dbl for 4 ppl), then peppers. Cook, stirring occasionally, until softened, 3-4 min. Add chorizo and remaining garlic. Cook, breaking up chorizo into smaller pieces, until no pink remains, 3-5 min.**

Add roasted potatoes, tomatoes, half the green onions and remaining parsley in the pan with chorizo. Stir together. Divide hash between bowls and top with caramelized onions. Dollop over aioli. Sprinkle over remaining green onions.

In Step 4, while chorizo cooks, heat a medium non-stick pan over medium-low heat. When hot, add 2 tbsp butter (dbl for 4 ppl) and swirl pan, until melted. Crack in two eggs (dbl for 4 ppl). Season with salt and pepper. Pan-fry, covered, until egg white is set 2-3 min. (NOTE: The yolk will still be runny! If preferred, pan-fry eggs using 1 tbsp oil — instead of butter.)