Bring the stock to a boil in a medium saucepan. Once boiling, add the grits and whisk constantly until they are fully mixed into the stock, about a minute or two. Reduce the heat to low and cover, stirring once or twice more, until the grits are thicker and creamy, about 5 minutes. Stir in about 1/2 to 2/3 cup of pimento cheese until creamy. Keep the grits over the lowest heat possible and take a few minutes to cook the eggs to your liking.