Combine the wild rice and broth in a saucepan and bring to a boil.

Reduce to a gentle simmer, cover, and cook until the grains are tender and many have split open to show their pale insides, 45-55 minutes.

Drain off any broth that hasn't been absorbed.

Meanwhile, brown the sausage in a large skillet over medium-high heat, breaking it into small pieces, until cooked through and crisp in spots, about 8 minutes.

Transfer the sausage to a plate with a slotted spoon, leaving the fat in the pan.

Add the butter and mushrooms to the skillet and cook without stirring for 3 minutes so they brown.

Stir the mushrooms and cook until golden, 3-5 minutes more.

Add the onion, celery, and thyme and cook until softened, about 6 minutes.

Stir in the pecans and cook 2 minutes to warm through.

Fold in the cooked wild rice and sausage and season to taste with salt and pepper.

Transfer to a buttered baking dish and bake, covered, at 350°F for 25-30 minutes.