1Split and mash the potatoes in a mixing bowl; set aside. The potato skins may be left on if desired.
2Melt the butter in a saucepan over medium-high heat; cook and stir the bell pepper, onion, and celery in the melted butter until they begin to soften, 5 to 7 minutes. Remove from heat and stir the milk into the mixture; pour the mixture over the mashed potatoes and stir to combine. The consistency should not be too runny. Allow the mixture to cool completely.
3Preheat an oven to 350 degrees F (175 degrees C).
4Add the crabmeat, Cheddar cheese, and dill to the potato mixture; season with salt. Lightly mix. Pour the beaten eggs into the mixture and stir to combine. If the mixture is too thin, bread crumbs or flour can be added to make more firm. Form the mixture into 24 small patties.
5Heat the olive oil in a large skillet over medium heat; cook the patties in small batches in the skillet until completely browned and crisp, 3 to 5 minutes per side. Do not flip until bottom is fully browned and crisp; this ensures the patties will not break. Transfer to a baking dish in the oven to keep hot until all are cooked. Serve hot.