Lightly grease a bowl. Knead dough together just until combined and smooth. Place in prepared bowl; cover and let rest in a warm place, 1 1/2 to 2 hours.

Roll and stretch dough to fit a 10"-x-15" pizza pan. Cover and let rest in a warm place, 25 to 30 minutes.

Preheat oven to 425 degrees F. Press fingertips into dough making small indentations. Drizzle oil over dough (allowing some to seep under dough). Top with apricots and goat cheese, pressing lightly into dough. Season with salt and pepper.

Bake until golden brown, 25 to 30 minutes. Cool, in pan, on a wire rack for 15 minutes.

Transfer to a cutting board. Top with prosciutto and arugula, and cut into 12 pieces.