Preheat a grill to medium. Stir together the grated garlic and olive oil in a small bowl, then brush on the cut side of the bread pieces. Top with the mozzarella, then the ricotta (about 4 small dollops per piece of bread). Sprinkle with the oregano, red pepper flakes and a pinch of salt. Scatter the chopped sun-dried tomatoes on top.
Place each piece of bread on an 18-inch-long sheet of heavy-duty foil. Bring the two short ends of the foil together and fold twice; fold in the sides to seal.
Grill the foil packets, covered, until the bottom of the bread is toasted and the cheese is melted, 8 to 10 minutes.
Meanwhile, toss the arugula, artichokes and a pinch of salt in a bowl. Carefully open the foil packets and top the pizzas with the prosciutto and arugula salad; drizzle with olive oil.
Use soft bread for foil-packet pizzas — it will get nice and toasted on the grill. Crusty loaves will end up too crunchy.