Cut the chicken into 2.5 cm (1 inch) cubes and season with the smoked paprika and salt. Rinse the rice.
Heat the oil in a large deep pot or Dutch oven with a lid over medium-high heat.
Brown the chicken for about 5 minutes, turning once. Add the onion and garlic and cook 2 minutes more.
Stir in the rice and broth, scraping up the browned bits. Bring to a boil over high heat, then cover, turn the heat to low and simmer for 15 minutes without lifting the lid.
Scatter the broccoli over the top, cover again and cook 5 minutes more, until the rice is tender, the broccoli is bright green and the chicken has reached 74°C (165°F).
Take off the heat, stir in the milk and grated cheddar until creamy, and season with pepper. Rest 2 minutes before serving.
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