Heat olive oil in a 3 quart nonstick sauté pan over medium heat. Add broccoli, garlic, 1/4 teaspoon salt, and pepper. Cook until the broccoli is tender, about 5 minutes, stirring occasionally. Transfer broccoli to a plate and set aside.
Add rice, vegetable stock, and 1/2 teaspoon salt. Stir. Bring to a boil over high heat, then cover with a lid and decrease to medium-low heat or lower to maintain simmer. Simmer for 30 minutes.
Uncover the pan and check that the rice is tender and done. Add cheddar cheese and stir with the rice until melted. Add broccoli and butter to the pan, stirring until the broccoli is heated and the butter is melted. Serve while hot.