Begin by placing your eggs in a single layer in a pot and cover them with cold water by an inch. Bring to a boil over medium-high heat, then reduce to low and simmer for 1 minute. Turn off the heat and let sit in hot water for 12 minutes.

Transfer the eggs to a bowl of ice water once cooking is complete. Cool for about 10 minutes to make peeling easier, peeling under running water if needed.

Combine 1 cup apple cider vinegar, 1 cup water, 2 tablespoons salt, and 1 tablespoon sugar substitute in a saucepan. Heat over medium, stirring until dissolved, then simmer for about 5 minutes.

Carefully place the peeled eggs into a clean glass jar or container. Pour the hot brine over them until fully submerged, adding extra vinegar or water if needed.

Seal with a tight lid and let cool to room temperature for about 30 minutes. Transfer to the refrigerator to pickle for at least 24 hours, preferably 48 hours for best flavor.