Cheese sauce: In a medium saucepan, melt butter over medium heat; stir in flour and cook, stirring constantly for 2 minutes. Whisk in milk, about 1/2 cup (125 ml) at a time until incorporated and lump free. Stir in Cheddar and pepper. Cover and keep warm.
Hash: Place potatoes in a medium saucepan and cover with cold water. Bring to a boil over high heat. Reduce heat and let simmer until potatoes are half cooked. Drain without rinsing and transfer to a plate; let cool for 5 minutes.
Place half of the potatoes in the bowl of a food processor; add half each of the leeks and bacon. Pulse until potatoes are finely chopped into pea-sized hash but being careful not to purée. Scrape mixture into a bowl if it is mostly pea-sized and pulse any large remaining chunks into same size to prevent over processing entire mixture. Repeat with remaining potatoes, leeks and bacon.
In a large nonstick skillet, heat oil over medium-high heat. Cook potato hash, stirring and flipping occasionally until golden brown. Keep warm on low heat.
In a medium saucepan, bring 2 inches (5 cm) of water to a gentle simmer. Crack 2 to 3 eggs individually into bowls. Stir water with a spoon to create a small whirlpool. Gently pour eggs into the simmering water and poach to desired doneness. Using a slotted spoon, transfer eggs to shallow dish and cover to keep warm. Repeat with remaining eggs.
For each serving, spoon one-sixth of the hash on a plate and top with 2 poached eggs. Ladle ⅓ cup (75 ml) of cheese sauce over eggs and hash. Serve garnished with sprinkling of parsley and paprika.
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