Preheat the oven to 375°F and grease a 9x13 baking dish.
Blanch the broccoli florets in boiling salted water for 2 minutes, then drain well. They should still be bright green and crisp.
Melt the dairy free butter in a large saucepan over medium heat and cook the onion for 4 minutes until soft. Add the garlic for 30 seconds, then stir in the flour and cook for 1 minute.
Slowly whisk in the chicken broth and oat milk and simmer for 3-4 minutes until thickened. Remove from heat and stir in the nutritional yeast, Dijon mustard, smoked paprika, salt, pepper, and 1 cup of the dairy free cheddar until melted.
Fold the rice, chicken, and broccoli into the cheese sauce and spread the mixture evenly into the baking dish.
Sprinkle the remaining cheddar over the top. Toss the panko with the olive oil and scatter it over the cheese.
Bake for 25 minutes until bubbling and golden on top. Let it rest for 5 minutes before serving.