Bring chicken broth, bay leaves, and 1 bundle thyme to boil in medium saucepan over medium-high heat. Add the rinsed wild rice, cover, and reduce heat to low. Simmer until rice is plump and tender and has absorbed most liquid, 40 minutes (See Note 3). Keep covered to keep warm and set aside.
Rinse white rice in mesh strainer until water runs clear to remove excess starch and drain completely.
Heat butter in medium saucepan over medium-high heat, about 2 minutes. Add onion, carrot, and 1 teaspoon salt; cook, stirring frequently, until softened but not browned, about 4 minutes.
Add rinsed white rice and stir to coat grains with butter. Cook, stirring frequently, until grains begin to turn translucent, about 3 minutes. Add 2 1/4 cups boiling water and second thyme bundle to rice and return to boil. Reduce heat to low, sprinkle cranberries evenly over rice, and cover. Simmer until all liquid is absorbed, 18 minutes. Fluff rice with fork off heat.
Combine wild rice, white rice mixture, pecans, and parsley in large bowl. Toss with large spoon or rubber spatula and adjust seasonings with salt and pepper if needed. Serve immediately.
Divide fresh thyme into 2 bundles, each tied together with kitchen twine.
Toast pecans in small dry skillet over medium heat until fragrant and lightly browned, about 6 minutes, then rough chop.
If wild rice still has a little liquid on bottom of pan: Drain rice in mesh strainer to remove excess liquid. Return rice to now-empty saucepan. Cover to keep warm and set aside.