Scrub and trim potatoes, leaving the peels on, and place in a pot of lightly salted water just to cover.
Simmer over medium to low heat until they are just fork-tender. Do not overcook the potatoes, which should still be firm.
While the potatoes are cooking, make the bechamel and roll out the pastry dough.
In a medium saucepan with a heavy bottom, melt the butter over medium heat. Do not let the butter brown.
Add the flour all at once and quickly whisk until it is all incorporated with the butter into a thick paste. It will clump at first, then loosen and bubble as the roux cooks.
Whisk continuously over medium-low heat for several minutes. Do not brown the roux. Reduce heat if needed.
Slowly pour in the milk, whisking vigorously as you add it until the sauce is smooth. It may clump at first, but don't stop stirring and it will loosen up and smooth out.
Simmer over low to medium low heat until the sauce thickens, stirring frequently so that the bechamel doesn't burn.
Whisk the salt, pepper, nutmeg, minced garlic and dill into the thickened bechamel sauce.
Remove the thickened sauce from the heat, and whisk in the softened goat cheese and stir until smooth, then add the heavy cream or creme fraiche and stir again until incorporated.
Crack the eggs one at a time in a bowl, and whisk in a spoonful of the hot bechamel mixture. Add this egg and sauce to the pot of goat cheese sauce, whisking as you add the egg until it is smooth and there are no lumps.
Repeat this for the second egg, then cover and keep the sauce in a warm place but off direct heat.
If you like, you can peel the potatoes or leave the skins on if they are thin (these will give you slightly more rustic tarts, but keeps the nutrition and fiber from the peels in your dish).
Slice the potatoes into even ¼" thick slices.
On a lightly floured surface, roll out the pastry crust ¼" thick.
Using a pastry cutter, pizza wheel, or paring knife, or a large circle cutter, cut out rough circles about an inch larger than the diameter of your tart rings or pans.
Roughly fit the crusts into the rings or tart pans. Avoid re-rolling the pastry dough by using scraps to fill out any holes or gaps in the sides or bottoms of the tartlet crusts.
Use a fork to gently prick the base of the tart crusts, especially if you are using puff pastry.
Divide the sliced potatoes among the tart pans, and line the bottoms of them with a single layer of cooked potato.
You can trim the potatoes to fit and get even coverage, or layer them if you have more than will fill the pans in a single layer.
Use a ladle to divide the goat cheese and egg bechamel sauce among the pans.
Spread the sauce gently to cover the potato slices and completely fill the tart shells.
Bake the tartlets at 400℉ for 25 minutes, then lower the heat to 350℉.
Bake another 15-20 minutes, or until the crusts are lightly golden and the filling is set and beginning to color.
Let the tarts cool in the rings or pans just until the filling is setting up. Once the rings or tart pans are cool enough to handle (but still warm), remove the tartlet rings or the sides from the tart pans.
