Combine brown rice, wild rice and chicken broth in a saucepan and bring to a boil. Cover, reduce heat to a simmer and cook until all water is evaporated and rice is fully cooked, about 45 to 55 minutes. Remove from heat and cool completely.
When rice is cool, add orange slices, basil, red onion, pistachios and orange zest; mix to incorporate.
Combine the red wine vinegar, olive oil, orange juice, mustard, honey and salt in a metal bowl and whisk to incorporate.
Pour over rice mixture and toss to incorporate.