Let 1 tablespoon unsalted butter sit at room temperature until softened, about 20 minutes. Coat 4 (4-ounce) Mason jars or 4 coddlers with the softened butter.

Place 1 (4-ounce) Mason jar or 1 coddler in a large saucepan. Pour in enough water to reach just below the rim. Remove the jar or coddler and bring the water to a boil over medium-high heat. Meanwhile, finely chop 3 slices cooked bacon (or 1 slice ham) and mince ¼ bunch fresh chives until you have 4 teaspoons.

Spoon the following into each jar or coddler: 2 teaspoons of the heavy cream, 2 teaspoons chopped bacon (or ham), and ½ teaspoon minced chives. Crack 1 egg on top of each, then season with a generous pinch of kosher salt and ground white or black pepper. Add 1 more teaspoon heavy cream on top of each egg. Secure with lids.

When the water is boiling, use tongs to transfer the jars or coddlers into the boiling water. Reduce the heat to medium and simmer until the egg whites are set and the yolk is still soft, 8 to 9 minutes. Carefully remove the jars from the hot water with tongs. If you prefer a more set yolk, turn off heat and allow to rest for 1 or 2 minutes more with the lids on before removing from the water.

Unscrew the lids with a dishtowel, as the jars will be hot. Garnish the eggs with the remaining minced chives and chopped bacon. Serve immediately with buttered toasted soldiers and more salt and pepper if desired.