In a small bowl, dissolve the brewer's yeast in 1 1/2 cups warm water. The yeast should bubble slightly as it dissolves. If not, the yeast is stale and you will need to try again with fresh yeast. In a medium-sized bowl, combine the dissolved yeast and the flour, and season with salt and pepper. Knead the resulting dough, adding more water if necessary to create a springy, paste-like dough. Cover with a damp kitchen cloth and leave for 2 hours to rise in a warm place (such as the tip of the refrigerator).
In the meantime, cut the anchovy fillets into tiny pieces, and place them in a bowl. Place the ricotta in a separate bowl. Using a fork, crush the ricotta so that no large lumps remain, stir in anchovies.
When the dough has risen, dampen your palm slightly, and break off a small (1-inch) piece of dough. Using the fingertips of your other hand, pat this dough into an open shell-like shape. In the resulting hollow, spoon 1 tablespoon of ricotta filling. Pull up the edges of the dough so that it covers the filling and forms a closed and rounded shape. Set aside. Repeat with the remaining dough and filling.
Fill a deep pot no more than halfway with extra-virgin olive oil. Heat oil over medium-high heat until it reaches a temperature of 360 to 365 degrees F. The oil should remain at or around this temperature throughout the cooking process. Working in small batches of 6, carefully lift the ricotta balls and place them in the hot oil. Fry the fritters until golden brown. Using a slotted spoon or spatula, remove the finished fritters to a plate lined with paper towels. Drain on paper towels as they cook. Continue this process until all the fritters are cooked. Serve hot, garnished with parsley and pecorino.