Preheat oven to 350 degrees.
1. Place rice, water, and salt in a medium saucepan and bring to a boil over medium high heat. Simmer until the grains open all the way. Drain rice and set aside.
2. Cook chorizo in a small saucepan over medium heat until the fat is rendered and the chorizo is a little crisp. Drain and set aside.
3. Melt butter in a large saucepan over medium heat. Add onion, carrots, and celery, cook for about 4 minutes. Add garlic and cook for 1 more minute.
4. Add cooked rice, cooked chorizo, bread, goat cheese, parsley, thyme, and stock. Stir to combine. The mixture should be quite wet. Add a little more stock or water if needed. Season to taste with salt and pepper.
5. Transfer to a buttered baking dish and bake uncovered in oven until golden brown and heated through, about 25 to 30 minutes.