In a large pot or Dutch oven over medium heat, cook the diced bacon for 6-8 minutes until crispy and the internal temperature reaches 75°C. Remove with a slotted spoon and set aside on kitchen paper, leaving the rendered fat in the pot.

Add the butter to the bacon fat, then sauté the onion and celery for 5 minutes until softened. Add the garlic and cook for another minute until fragrant.

Add the diced potatoes, chicken stock, thyme, and smoked paprika. Bring to a boil, then reduce heat and simmer for 18-20 minutes until potatoes are fork-tender.

While the soup simmers, prepare the soft-boiled eggs. Bring a small pot of water to a rolling boil. Gently lower the eggs into the water and cook for exactly 7 minutes for a jammy yolk.

Transfer the eggs immediately to an ice bath for 3 minutes, then carefully peel and set aside.

Using a potato masher, roughly mash about half of the potatoes in the soup, leaving some chunks for texture. Stir in the milk and double cream, heating through for 3-4 minutes without boiling.

Season the soup with salt and pepper to taste, then stir in half of the cheddar cheese until melted.

Ladle the soup into four warm bowls. Halve the soft-boiled eggs and place two halves in each bowl. Top with reserved crispy bacon, remaining cheddar, and a generous amount of fresh chives. Serve immediately.