For Filling:
Slice carrots into coins. Place sprigs of thyme over carrots and steam until cooked through, but not mushy. Reserve 2 T of hot water used for steaming. (You can also boil carrots, submersing in water. I Set 1 cup of coins aside to top the tarts. Make sure you have enough to cover the top of the tart. Saute sliced leeks in olive oil. Add salt.
Puree carrots (except those reserved to top tart) with 1 cup parmgiano-regianno, salt, pepper, eggs, chopped parsley.
Assembly
Once dough is pressed into tart pans, layer with leeks, carrot puree, carrot coins. Top with remaining cheese. Bake until tarts are set, about 25 minutes at 350.
Note: There was marjoram in filling; I deleted. There was a layer of breadcrumbs on bottom of tart. I found this to be unnecessary.