Toast the pecans in a dry 3-quart / 2.8 L saucepan over medium heat, stirring, for 3 to 4 minutes until fragrant and lightly darkened. Transfer to a plate.
Rinse the wild rice in a fine-mesh sieve under cold water until the water runs mostly clear.
Add the olive oil to the same pot over medium heat. Add the onion and celery, cook 5 to 6 minutes until softened.
Stir in the garlic and cook 30 seconds until fragrant.
Add the rinsed rice, stir to coat in the oil, and toast for 1 to 2 minutes.
Pour in the broth and add the thyme, salt, and pepper. Bring to a boil, then reduce heat to low and cover.
Simmer for 45 to 50 minutes until the grains split open and most of the liquid is absorbed. Check at 45 minutes; if the rice is still tight and pale, continue simmering in 5-minute increments rather than raising the heat.
Remove from the heat, scatter the cranberries over the rice, cover, and let stand 5 minutes.
Fluff with a fork and fold in the toasted pecans and parsley.
Taste, adjust salt and pepper, and serve warm.