Preheat oven to 450ºF. Remove pizza doughs from bags and let soften at room temperature (see recipe tip). Pat chicken dry with paper towel; season all over with 1 teaspoon salt and pepper. Heat 1 tablespoon olive oil in a large pan over medium-high heat. When oil is shimmering, add chicken (see recipe tip). Sear until cooked through and no longer pink, about 6 minutes per side. Transfer chicken to a plate and set aside; reserve pan.

While chicken cooks, rinse chives and thinly slice. Halve lemon. Mince garlic. In a medium bowl, whisk together mayonnaise, .25 cup Greek yogurt, half of chives, juice of .5 lemon, .25 teaspoon salt, and pepper as desired (save remaining lemon and yogurt for another recipe). Set ranch aside until ready to serve.

Line 2 baking sheets with parchment papers and rub each with 1 teaspoon olive oil. Sprinkle flour onto a clean, dry surface, coating a rolling pin or your hands with a thin layer. Roll or stretch doughs into rectangular shapes, rotating frequently and working from center to edges, until .25-inch thick. Add doughs to prepared sheets, gently stretching to reach edges of sheets.

Rub 2 teaspoons olive oil on top of each dough. Sprinkle over blue cheese and mozzarella, leaving a .5-inch border. Bake until crusts are crisp and light golden and cheese is bubbling, 12-15 minutes. If the baking sheets are on 2 different racks, switch them halfway through to ensure the crusts bake evenly.

While pizzas bake, shred rested chicken using 2 forks or roughly chop. Wipe pan from chicken clean and add butter over medium heat. When butter is foamy, add garlic and cook, stirring, until fragrant, 1-2 minutes. Remove pan from heat and stir in Sriracha (you could use less, but a little spiciness is what makes this Buffalo sauce!). Add shredded chicken and toss to coat with sauce.

Scatter Buffalo chicken over baked pizzas. Drizzle over Greek yogurt ranch, or serve alongside for dipping. Garnish with remaining chives. Cut pizza into slices and enjoy with fellow pizza-lovers!