Boil the eggs for exactly 6 minutes for a jammy yolk. Transfer to an ice bath, then peel and set aside.
Cook the pasta until al dente. Reserve 1/2 cup (120ml) pasta water, then drain.
Cook the chopped bacon 5 to 6 minutes, until crisp. Remove with a slotted spoon, leaving the fat in the pan.
Add the garlic to the bacon fat and cook 30 seconds, until fragrant.
Add the bourbon extract and brown sugar. Simmer 2 to 3 minutes, until reduced by about half.
Stir in the heavy cream. Simmer gently 3 to 4 minutes, until the sauce coats a spoon.
Remove from heat. Stir in the Parmesan until smooth, loosening with pasta water as needed.
Add the pasta and bacon to the sauce, tossing to coat. Season with salt and pepper.
Halve the peeled eggs and arrange over the pasta. Finish with chives and extra Parmesan.