Make the pizza dough: in the bowl of a stand mixer or in a mixing bowl, dissolve the yeast in the water. Stir in the honey. Let sit 2 to 3 minutes, until cloudy. Stir in the olive oil.
If using a stand mixer, combine the flour and salt and add all at once to the yeast mixture. Mix with the paddle attachment just until combined. Swap out the paddle for the hook attachment, then continue mixing the dough at low speed for 2 minutes. Increase to medium speed and knead until the dough clusters around the hook, about 5 minutes, steadying the machine if it moves. Turn out onto a clean work surface and knead by hand until smooth and elastic, 2 to 3 minutes.
Alternatively, put the flour and salt in the work bowl of a food processor with the stainless-steel blade. Pulse a couple of times. With the machine running, pour in the yeast mixture and process until the dough forms a ball that rides on the blade. Turn out onto a clean work surface and knead by hand until smooth and elastic, 2 to 3 minutes. Transfer the dough to a clean, lightly oiled bowl and turn to coat. Cover tightly with plastic wrap and leave in a warm spot to rise for 30 minutes to 1 hour.
Divide the dough into 4 balls, shaping each by pulling down on the sides and tucking each pull underneath, working around each ball 4 or 5 times. Then, on an unfloured surface, roll the ball under your palm until smooth and firm, about 1 minute. Put the balls on a tray, cover with a damp towel, and leave to rest for 30 minutes.
Place a pizza stone in the oven and preheat to 500ºF.
Meanwhile, place a ball of dough on a lightly floured surface. While turning it, press down on the center with the heel of your hand, gradually forming a circle that’s about 8 inches in diameter. With your fingertips, pinch a raised rim along the outside of the circle. Repeat with the remaining balls. Brush with a little olive oil.
Sprinkle the pizzas evenly with fontina and mozzarella. Using a lightly floured pizza peel or a rimless baking sheet, carefully slide each pizza onto the baking stone, being cautious with the very hot oven. Bake until the crust is nicely browned, 10 to 12 minutes. Carefully remove with the peel or baking sheet and transfer to a cutting board.
In a mixing bowl, toss the arugula with olive oil and vinegar; arrange it on top of the pizzas with the prosciutto. Sprinkle with Parmesan. With a pizza cutter or a large, sharp knife, cut each pizza into 4 slices. Serve immediately.