Preheat the oven to 140°C convection (approximately 275°F). Combine the crumbled yeast, flour, semolina, olive oil and sugar in a bowl and knead with the dough hook of a mixer until smooth. Cover and let rise in a warm place, free from drafts, until doubled in bulk.
Divide the dough into 20 portions. Roll each portion on a floured surface into thin sticks about 20-25 cm (approximately 7 1/2–9 1/2-inch) long and place on a parchment paper-lined baking sheet, leaving space between each. Let dough rise again, and then bake until crisp, covering with aluminum foil if necessary to prevent overbrowning, 25-30 minutes.
Remove the baked grissini from the oven and let cool. Trim arugula, rinse and spin dry. Wrap each breadstick with some arugula and a slice of prosciutto and place in serving glasses. Serve.