Bring a large pot of lightly salted water to a boil. Cook bow-tie pasta at a boil, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain and let cool.

Meanwhile, place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add broccoli, cover, and steam until tender, 4 to 6 minutes. Drain and let cool.

Cut cheeses into small cubes and combine in a large bowl with pasta, broccoli, ham, cherry tomatoes, olives, and pepperoni. Mix in the dressing. Season with salt, pepper, oregano, and paprika. Refrigerate until ready to serve.