Combine water, sugar, and yeast in the bowl of a standing electric mixer, stirring until the yeast dissolves. Let sit until bubbly, about 5 to 10 minutes.

Add two cups flour, salt, and olive oil to the yeast mixture. Mix well with the paddle attachment until evenly combined. Add additional flour about 1/4 cup at a time until the dough clears the sides of the bowl.

Switch to the dough hook and knead until the dough is smooth and elastic, about 3 to 5 minutes. The dough should feels slightly tacky; if it's overly sticky, knead in a bit more flour. Transfer the dough into a lightly greased bowl, flipping it to coat the entire surface with oil. Cover with plastic wrap and let the dough rise until doubled in size, about one hour.

Generously grease the cups of a standard-sized muffin tin. Set aside. Preheat oven to 350° F.

Turn the dough out on an unfloured surface and divide it into 12 pieces roughly the same size.

Working with one piece at a time, shape the dough into 4 by 6-inch rectangles. Spread 1 teaspoon tomato paste over the dough with the back of a spoon, leaving a border at least 1/4-inch all the way around the edge. Tear 1/3 of a piece of prosciutto into small pieces and sprinkle them over the tomato paste. Add about 2 teaspoons minced olives, spreading them evenly over the rectangle. Top with two scant tablespoons mozzarella and tamp the toppings down lightly with your fingers.

Working from the rectangle's wide edge, carefully roll up the dough and seal the edges together. Give dough a gentle roll with your fingers to even it out and lengthen it slightly. Wrap the dough into a tight snail and place it in the muffin tin, pressing it down to fill the cup. Repeat with remaining dough.

Sprinkle remaining cheese evenly over the tops of the pizza rolls. Bake until the rolls feel firm and the cheese on top turns deep golden brown, about 25 to 30 minutes. Serve warm.