Brown the chorizo sausage links in a large, high-sided skillet or frying pan over medium heat for 2-3 minutes per side. Once browned, remove sausage from skillet and cut into bite-sized pieces. Set aside.
Add olive oil to the skillet and add the chopped carrot, celery, and onion. Season with salt and black pepper, to taste, and stir to combine. Cook for 4-5 minutes, stirring occasionally until the vegetables soften and develop some color.
Return the chopped chorizo to skillet, along with the chicken stock, red lentils, diced tomatoes, oregano, garlic powder, thyme, bay leaves, and Parmesan rind, if using.
Stir to combine and increase heat to medium-high. Bring to a boil, then immediately reduce heat to medium-low. Cover with a tilted lid and simmer for 20-25 minutes, or just until the lentils are tender.
Remove from heat and discard the bay leaves and remaining Parmesan rind. Taste and adjust seasonings as needed. Stir in fresh basil.
Serve immediately, topped with some freshly grated Parmesan cheese, if desired.