Melt the butter in a large skillet (that has a lid) or Dutch oven over medium heat. Add the rice and cook, stirring regularly, until the rice is browned – about 2-3 minutes. Add the onion, celery and carrot; cook, stirring regularly, until the vegetables start to soften – about 4 minutes.
Add salt and pepper, to taste. If you’re using salted chicken broth, you probably won’t need too much extra salt. If you’re using low-sodium or homemade unsalted broth, you may need up to ½ - ¾ teaspoon of salt.
Add the broth to the skillet with the rice and vegetables. Add the bay leaf; bring the liquid to a simmer, then reduce the heat to low, cover the skillet, and let the rice simmer for 18-20 minutes. Once the liquid has been absorbed and the rice is tender, turn off the heat, discard the bay leaf, fluff the rice with a fork, and stir in the fresh parsley and toasted almonds.