Preheat the oven to 350°F (175°C) and line a baking sheet with parchment or lightly grease it.
Cut each avocado in half lengthwise and remove the pits. Scoop the flesh from one whole avocado into a large mixing bowl. If desired, scoop a small amount from the centers of the remaining halves to enlarge the wells and add that flesh to the bowl.
Add the shredded chicken, 1/3 cup of the grated cheddar, chopped cherry tomatoes, sliced green onions, chopped cilantro, chili powder, smoked paprika, garlic powder, cumin, and a pinch of salt and pepper to the bowl with the avocado. Mash and stir until well combined and the avocado acts as a binder.
Spoon about 1/4 cup of the chicken mixture (or fill to taste) into each avocado half using a spoon or ice cream scoop. Place the filled avocados on the prepared baking sheet, then sprinkle the remaining approximately 1/3 cup of cheddar evenly over the filled halves.
Bake for 15 to 20 minutes, until the filling is heated through and the cheese is melted and bubbly. The avocado flesh may darken slightly from baking.
While the avocados bake, whisk together the Greek yogurt, sriracha, and lime juice until smooth to make the drizzle.
Remove the avocados from the oven, drizzle with the sriracha-yogurt sauce, and sprinkle with extra cilantro and sliced green onions if desired. Serve immediately.
