Bring a large pot of water to a boil, carefully lower in the eggs, and cook for 10 minutes.

Transfer the cooked eggs immediately to a bowl of ice water for 5 minutes, then peel completely.

In a medium saucepan over medium heat, combine the apple cider vinegar, white sugar, brown sugar, garlic powder, turmeric, and cayenne pepper.

Bring the syrup to a boil, stirring until the sugars dissolve, then add the sliced jalapeños and simmer for 5 minutes.

Pack the peeled eggs tightly into a clean 1-quart wide-mouth mason jar.

Carefully pour the hot brine and jalapeño slices over the eggs, ensuring everything is submerged with 1/2-inch headspace.

Let the jar cool to room temperature, seal tightly with a lid, and refrigerate for at least 7 days before serving.