preheat oven to 425 °F (220 °C) and toss hash browns with olive oil, salt, and pepper until coated

spread potatoes in a single layer on a baking sheet and roast until deeply golden and crisp, flipping halfway through

while potatoes roast, arrange bacon on another sheet and bake until crisp, then crumble into bite-sized pieces

set up a double boiler and whisk egg yolks with lemon juice, vinegar, and cayenne until pale

slowly drizzle warm melted butter into the yolks while whisking to form a thick, glossy Hollandaise, keep warm

bring a pot of water to a gentle simmer, add a splash of vinegar, then gently slide eggs in and poach for runny yolks

pile hot hashed potatoes onto plates, sprinkle with cheddar and mozzarella so warm heat begins to soften them

ladle rich Hollandaise generously over the cheese and potatoes

top each serving with crumbled bacon and one or two poached eggs

finish with a scatter of fresh chives or parsley and serve while everything is still warm