Bring broth to a boil in a medium saucepan over high heat. Stir in mushroom and wild rice. Return to a boil. Reduce heat to very low, cover, and simmer until the rice has "blossomed" and is just tender, 45 to 55 minutes. Drain any remaining liquid and transfer the rice to a serving bowl.
Meanwhile, toast almonds in a small dry skillet over medium-low heat, stirring constantly until golden brown and fragrant, 2 to 3 minutes. Transfer to a plate to cool.
About 5 minutes before the rice is done, melt butter in a medium nonstick skillet over medium heat. Add scallions and cook, stirring often, until softened and still bright green 2 to 3 minutes.
Stir the scallions, almonds, and pepper into the rice. Serve warm.