Preheat the oven to 375°F. Lightly grease a 9x13-inch baking dish.
Blanch the broccoli: bring a large pot of salted water to a boil, add the broccoli florets, and cook for exactly 2 minutes. Drain immediately and rinse under cold water to stop the cooking. The broccoli should still be bright green and firm — it will finish cooking in the oven. If using frozen broccoli, thaw completely and squeeze out excess water.
Heat the olive oil and 2 tbsp butter in a large skillet or saucepan over medium heat. Add the diced onion and cook for 4 to 5 minutes until softened. Add the garlic and cook for 30 seconds. Add the flour and stir constantly for 1 to 2 minutes until lightly golden — this cooks out the raw flour taste.
Slowly pour in the chicken broth while whisking constantly to prevent lumps. Then whisk in the heavy cream. Add the garlic powder, onion powder, smoked paprika, salt, pepper, and red pepper flakes if using. Bring to a gentle simmer and cook for 3 to 4 minutes, stirring frequently, until the sauce thickens enough to coat the back of a spoon. Remove from heat.
Stir 1.5 cups of the shredded cheddar into the sauce until melted and smooth. Add the shredded rotisserie chicken and blanched broccoli and stir to coat everything evenly. Taste and adjust salt.
Transfer the mixture to the prepared baking dish and spread evenly. Sprinkle the remaining ½ cup of cheddar over the top.
In a small bowl, toss the panko breadcrumbs with 1 tbsp melted butter and a pinch of salt. Scatter evenly over the top of the casserole.
Bake uncovered for 25 to 30 minutes, until the sauce is bubbling around the edges and the panko topping is golden brown. Let rest for 5 minutes before serving.