Preheat oven to 450°F. Roll out or press pizza dough into pan and set aside.
Add olive oil to a sauté pan and set over medium-high heat. Add the ground beef and onion and cook, breaking up meat into small pieces, until no pink remains. Mix together salt, paprika, and pepper, and sprinkle over the meat and onion. Stir well to coat with the spices. Drain excess grease from meat and set aside.
In a small bowl, stir together the ketchup, mayonnaise, mustard, and pickle relish until smooth. Add more mayo or mustard to taste.
Spread sauce on the pizza dough in an even layer, leaving an empty edge all around. Scatter on half the mozzarella and half the cheddar. Top with ground beef mixture, then the remaining cheeses. Arrange pickle slices as desired.
Bake on the bottom rack for 12-15 minutes, until crust is golden and cheese is melted. Let cool slightly before cutting and serving.