Fill a large bowl with water. Add rice and let soak for 10 minutes; drain and rinse until water runs clear.

Heat 1/4 cup butter and 2 tablespoons olive oil in a skillet over medium heat; cook and stir orzo in hot butter-oil mixture until lightly browned, about 5 minutes. Add drained rice and increase heat to medium-high. Cook and stir orzo-rice mixture until rice is coated in butter-oil mixture and starts to turn translucent, about 5 minutes.

Pour 4 cups water over rice mixture and add salt; stir and bring to a boil. Cover the skillet, reduce heat to low, and simmer until rice is fluffy and tender yet firm, about 20 minutes.

Meanwhile, heat remaining 2 tablespoons olive oil in a separate skillet over medium heat; cook and stir almonds until toasted and fragrant, about 5 minutes. Stir in remaining 1/4 cup butter and tahini until almonds are evenly coated.