Rinse broccoli crowns, trim stems, and quarter.
Blanch broccoli in a large sauce pot of salted water for 45 seconds, then remove from pot, strain, and cool with cold water.
Line a large baking sheet with aluminum foil and place in oven preheated to 425 degrees Fahrenheit for 10 minutes.
Remove baking sheet from oven, add broccoli, then toss with olive oil, salt, pepper, paprika, and crushed red pepper; roast for 20 minutes, flipping halfway through.
In a small saucepan on medium-high heat, sauté minced garlic in coconut oil for about 1 minute until tender.
Remove broccoli from pan, pour garlic and coconut oil over broccoli, and finish by sprinkling with nutritional yeast.