Melt butter in a large pot over medium heat. Add onion and cook until soft and translucent, 5-7 minutes. Stir in garlic and cook until fragrant, about 30 seconds.
Add rice and cook, stirring, until rice is fragrant and lightly toasted, about 3 minutes. Pour in stock, season with salt and pepper and bring to a boil.
Reduce heat to low, cover and cook without stirring, for 12 minutes. Add the broccoli, parsley and mint on top of the rice, cover the pot, and continue to cook until the rice is tender and all of the liquid has been absorbed, about 5 minutes. Remove from heat and let stand, covered, until broccoli is crisp-tender, 5-7 minutes. Fluff and mix with a fork. Serve warm.