In a large bowl, mix the flour and salt. Add the cold butter and work it into the flour with your fingers until the mixture looks like coarse crumbs. Add the egg and gently mix just until a soft dough forms. Shape into a ball, wrap tightly, and refrigerate for 30 minutes.
Heat the olive oil in a large skillet over medium heat. Add the pumpkin and cook for about 5 minutes, stirring occasionally, until lightly golden. Add the onion and garlic and cook for another 2 to 3 minutes until softened and fragrant. Remove from heat and let cool slightly.
In a large bowl, whisk together the heavy cream, eggs, and shredded cheese. Stir in the thyme, smoked paprika, nutmeg, salt, and black pepper. Gently fold in the cooked pumpkin mixture.
Preheat the oven to 350°F. Lightly grease a 10- to 11-inch quiche or tart pan. Roll out the chilled dough on a floured surface and press it into the pan. Prick the bottom with a fork. For a crisper crust, line with parchment paper, fill with pie weights, and bake for 10 minutes. Remove weights before filling.
Pour the pumpkin filling into the warm crust and sprinkle the feta evenly over the top. Bake for about 30 minutes, or until the center is set and the top is lightly golden. Allow to cool slightly before slicing.
