Mix the flour and semolina in a bowl. Add the eggs and egg yolk, mix, knead for approx. 15 mins. to form a smooth dough. Shape into a ball, then leave to rest for approx. 30 mins. at room temperature under a bowl rinsed in hot water.
Combine the ricotta, cheese, thyme, lemon zest and lemon juice, season.
Roll out the dough in batches to approx. 2 mm thick, cut out approx. 50 circles (each approx. 10 cm in diameter). Keep the dough covered at all times to prevent it from drying out. Brush the pieces of dough with a little egg white, place 1 tsp of filling in the middle of each circle. Gather the edges together, press together above the filling, pressing out any trapped air. Place the fagottini on a lightly floured tea towel.
Cook the fagottini in batches in simmering salted water for approx. 7 mins. Remove the fagottini with a slotted spoon, transfer to a bowl, add the butter and thyme, mix and keep warm.