Preheat the oven to 375 degrees and line a baking sheet with parchment paper.
In a large bowl, combine the ground beef, mushrooms, thyme, breadcrumbs, egg, garlic, salt, and pepper. Mix until just blended.
Divide the mixture into eight equal portions and shape each into a small loaf. Place the loaves on the prepared baking sheet.
Bake the meatloaves for 25 minutes, or until they reach an internal temperature of 160 degrees.
While the meatloaves bake, heat the olive oil in a medium saucepan over medium heat. Add the carrot and cook for 3 minutes.
Stir in the wild rice and vegetable broth. Bring to a boil, then reduce to a simmer, cover, and cook for 40 minutes until the rice is tender and the liquid is absorbed.
Let the meatloaves rest for 5 minutes before serving with the wild rice pilaf.