In a large bowl, mix together the mashed potatoes, egg, garlic, parsley, thyme, green onions, flour, salt, pepper, and 1/4 cup of the parmesan cheese.
Place the remaining 1/4 cup of parmesan in a wide shallow bowl, Using 1/4 cup as your guide, divide the potato mixture into 8-10 equal portions and form them into rounded, flattened patties.
Dredge the potato cakes in the parmesan and then refrigerate for at least 20 minutes.
In a small bowl, whisk the sour cream, dill, and lemon juice and season to taste with salt.
In a large skillet over medium heat, add 3 tablespoons of the oil. Working in batches and adding more oil as you need it, cook the potato cakes until golden brown, about 2 minutes per side.
Garnish with the dill crema and serve warm.