Heat olive oil over medium heat in a large Dutch oven. Add chopped shallots and cook for 2 minutes, stirring frequently until they soften and release a gentle aroma.
Add diced celery and carrots and cook for 3 to 4 minutes, stirring often until they begin to soften and pick up a bit of color.
Pour in chicken broth to build your chicken pasta soup base, then tuck in bay leaves, rosemary, thyme, salt, and pepper. Bring to a boil, lower heat to maintain a steady simmer, and cook uncovered for 20 minutes so the flavors meld.
Fish out the bay leaves, stir in acini di pepe pasta, and return to a gentle simmer. Cook for 8 to 10 minutes until the pasta is tender but still holds its shape.
Fold in diced chicken or turkey along with the remaining rosemary and thyme. Stir until the meat warms through, then remove the pot from the heat.
Taste the broth and sprinkle in more salt and pepper if you prefer a bolder flavor, adding gradually to keep the balance right.
Cover the pot and let the soup sit off the heat for 15 minutes. This pause deepens the flavors before serving.