Melt butter in a large stock pot over medium-low heat. Add onion; cook until translucent 8-10 minutes. Add garlic; cook 1-2 minutes, stirring occasionally so as not to burn.
Increase heat to medium-high. Add both rices and thyme; cook 1 minute, stirring frequently.
Stir in vegetable broth, salt, pepper, and bay leaf; bring to a boil.
Reduce heat to low, cover, and simmer 1 hour or until rice is tender (do not stir).
Remove pan from heat; let stand 10 minutes. Remove bay leaf; discard.
Fluff rice mixture with a fork. Gently stir in parsley.