1. Toast nuts in a dry skillet over medium-high heat until fragrant, about 2 minutes. Set aside to cool.
2. Combine brown rice, wild rice, and chicken broth in a saucepan; bring to a boil. Cover, reduce heat, and simmer until all liquid is evaporated and rice is fully cooked, 45 to 55 minutes. Remove from heat and cool completely.
3. Transfer rice to a medium bowl. Add orange, basil, red onion, pistachios, and orange zest; mix.
4. In a small bowl, whisk together red wine vinegar, olive oil, orange juice, mustard, honey, and salt. Pour dressing over the rice mixture and toss.