Preheat the oven to 425°F (218°C) and lightly grease two baking sheets.
In a large bowl, combine the shredded chicken, 1/3 cup plain Greek yogurt, 1/2 cup buffalo sauce, 2 tablespoons chopped fresh chives, 2 tablespoons dried parsley, 2 teaspoons dried dill, 1 teaspoon onion powder, 1 teaspoon garlic powder, and a pinch of kosher salt.
Stir in 1 cup shredded cheddar and 1/4 cup crumbled blue cheese until evenly distributed.
Place an egg roll wrapper on a clean surface and spoon about 2 tablespoons of filling near the bottom third of the wrapper.
Brush water around the edges of the wrapper, fold the bottom up over the filling, fold in the sides, then roll tightly to seal. Repeat with remaining wrappers and filling.
Place assembled egg rolls on the prepared baking sheets and brush each lightly with olive oil.
Bake for 10–12 minutes, then flip the egg rolls and bake another 8–10 minutes until golden brown and crisp.
While the egg rolls bake, make the cilantro-lime ranch: combine 1 cup sour cream or plain Greek yogurt, 3/4 cup finely chopped cilantro, 1 tablespoon chopped fresh chives, 1 teaspoon garlic powder, 1 teaspoon onion powder, and juice from 2 limes in a jar and shake or stir until smooth.
Serve the baked buffalo chicken egg rolls warm with extra buffalo sauce and the cilantro-lime ranch for dipping.