In a pan, sauté crushed garlic in butter over medium heat. Discard when golden and add cleaned and washed spinach. Sauté over medium heat, stirring often, until spinach is dry.
Set aside to cool. Mash caprino cheese with a fork and add to cooled spinach. Stir in grated Parmigiano and season with salt. With a rolling pin, roll the dough into 8 circles. 4 should be at least as big as the tartlet pans and 4 should be slightly bigger in diameter.
Drape the bigger dough circles into 4 individual tartlet pans. Pour mixture into the shells and cover with the 4 remaining smaller circles, crimping the edges.
Prick the surface of the pies all over with a fork and brush with beaten egg. Cook in a preheated 400°F oven for about 20 minutes.