Place rice in a medium bowl and pour hot water (from the tap) over the top, covering it by about 2 inches, set aside, let stand for about 15 minutes.
After 15 minutes is up, use a spoon to gently stir the rice, to help release excess starch. Pour the water off, leaving just the rice in the bowl. Fill bowl with cold water, swish it around, and pour it off, repeat this 4-5 times until the water runs almost clear. Drain the rice in a fine-mesh strainer and set aside.
In a saucepan, over medium heat, melt butter then add the vermicelli pasta and cook about 3 minutes, stirring occasionally, until pasta is browned.
Add grated onion and minced garlic to the pan and cook for about 4 minutes, until onion is softened but not browned, stirring occasionally.
Add the rinsed rice and cook for about 3 minutes, stirring occasionally, until edges of rice begin to turn translucent.
Add broth, thyme, rosemary, and salt and bring to a boil.
Reduce the heat to low, cover your saucepan, and cook until all the liquid is absorbed, about 10 minutes.
Remove pan from heat, remove lid, fold a clean dish towel in half, and it place over the pan; replace lid. The dish towel will absorb some of the steam, giving you fluffy rice.
Let rice stand for 10 minutes. Fluff rice with fork, then stir in parsley, and serve.