Prepare the cauliflower rice: trim cauliflower and cut into florets.
Working in batches, pulse the florets in a food processor until they resemble grains of rice (about 20 short pulses); avoid overprocessing.
Heat a skillet over medium heat with 1 tablespoon olive oil. Add the cauliflower rice, season with salt and pepper, and sauté until tender, about 5–8 minutes. Transfer to a bowl and keep warm.
In the same (or a second) large skillet with a lid, heat 1 tablespoon oil over medium-high heat if using. Add the chicken pieces, season lightly with salt, and cook until browned on one side, then turn and cook until no longer pink, about 4–5 minutes per side.
Add the broccoli florets to the pan with the cooked chicken, cover, and steam until tender but still bright green, about 5–10 minutes; stir once or twice to prevent excessive browning.
Make the buffalo sauce: melt 2 tablespoons butter and whisk together with 1/4 cup hot sauce until combined.
Pour the sauce over the chicken and broccoli and toss to coat evenly.
Serve the buffalo chicken and broccoli over the prepared cauliflower rice (or regular rice if preferred).