Pulse spelt in a blender or food processor until coarsely chopped (all of the grains should be broken open but not ground to a powder). Combine spelt and 4 cups water in a large saucepan over medium-high; season with salt and pepper. Bring to a boil, reduce heat, and simmer, whisking occasionally, until spelt is tender and mixture is thick, 25–35 minutes. Whisk in Parmesan and butter. Add water by tablespoonfuls if needed to loosen. Just before porridge is done, cook eggs in a small saucepan of boiling water 6 minutes. Transfer to a bowl of ice water and let sit just until warm. Carefully peel and slice in half lengthwise. Heat oil in a small skillet over medium. Cook kimchi, tossing, just until slightly darkened and warmed through, about 1 minute. Divide grain porridge among bowls. Divide kimchi and eggs over top.