Heat the oven to 375 degrees. Place the beets on a baking sheet and roast for 45 minutes until tender. Let them cool, then peel and slice into thin rounds.
In a food processor, pulse 1 cup of the walnuts until finely ground. Add the flour, butter, and salt. Pulse until the mixture forms a dough that holds together when pressed.
Press the dough into the bottom and up the sides of a 9-inch tart pan. Bake the crust for 15 minutes, then remove from the oven.
In a bowl, mash 4 ounces of the goat cheese with the eggs and cream until smooth. Stir in the thyme.
Chop the remaining 1/2 cup walnuts and fold them into the cheese mixture. Spread the filling into the baked crust.
Arrange the sliced beets over the top. Crumble the remaining 2 ounces of goat cheese across the surface.
Bake the tart for 25 minutes until the filling is set and lightly golden at the edges. Cool for 10 minutes before slicing.