Preheat the oven to 390 °F.
In a mixing bowl, combine 1 tsp undissolved yeast with 1/2 cup warm milk for 2 minutes.
Add 5.2 oz all-purpose flour, 1 tbsp olive oil, and 1/2 tbsp sugar to the mixing bowl. Mix until well combined, then cover and let rest for 10 minutes until a soft dough ball is formed.
In a cast-iron skillet, heat 1 tbsp olive oil over medium heat. Sauté 4 oz diced yellow onion until fragrant (about 2 minutes).
Add 4 oz diced white mushrooms to the skillet and sauté for 2 minutes.
Add 6 oz ground beef, 1/2 tsp ground black pepper, 1/2 tsp Italian seasoning, 1 tsp garlic powder, 1/2 tsp salt, and 1/2 tbsp Dijon mustard. Sauté until golden brown and fragrant (3 minutes).
Place the dough ball onto a floured surface (use 1.4 oz flour). Knead it into a 2mm-thick round.
Fold an inch of the edges towards the center.
Use a fork to prick the surface of the dough so it won't rise too much in the oven.
Bake the pizza dough for 10 minutes.
Remove the pizza base from the oven. Spread 1 tbsp mayonnaise over the base of the pizza.
Continue to spread 1 1/2 tbsp ketchup over the base on top of the previous layer of mayo.
Add the toppings: sautéed beef, 2 oz cherry tomatoes, and 2 oz sliced red onion.
Spread 1 1/2 oz shredded cheddar cheese and 1 1/2 oz shredded mozzarella cheese on top.
Bake at 440 °F for 5 minutes until the center is bubbly and the crust is golden brown.
Garnish cheeseburger pizza with 2 tbsp chopped parsley, cut into slices, and serve hot.