Rinse the rice under cold water until the water runs clear. Drain well.
Heat olive oil in a pan over medium heat.
Add the gluten-free orzo and toast for 2–3 minutes, stirring, until golden brown.
Stir in onion, sautéing for 3–4 minutes until softened. Add garlic and cook for 30 seconds until fragrant.
Stir in the rinsed rice and cook for another 1–2 minutes.
Pour in the broth, add salt, pepper, turmeric, and thyme, and bring to a boil.
Reduce heat to low, cover, and simmer for 15–18 minutes until the rice and pasta are tender and the liquid is absorbed.
Remove from heat and let sit, covered, for 5 minutes.