In a small bowl, combine salt, Italian seasoning, black pepper, and red pepper flakes. Add the cubed chicken breast and toss until all pieces are evenly coated with the seasoning mixture. Set aside at room temperature while you prepare the aromatics—this allows the seasonings to penetrate the meat slightly before cooking.
Heat olive oil in a large heavy-bottomed pot over medium-high heat until shimmering. Working in batches if needed to avoid crowding, add the seasoned chicken and sear for 3-4 minutes, stirring occasionally, until the exterior is golden and cooked through. Transfer the cooked chicken to a clean plate. I like to let the chicken develop that golden crust—it adds depth to the final broth that you can't get any other way.
In the same pot with the remaining oil and browned bits, add the diced onion and cook for 4-5 minutes over medium heat, stirring occasionally, until softened and beginning to caramelize. Add the minced garlic and cook for another minute until fragrant. This builds a flavorful foundation for the chowder.
Pour the chicken broth into the pot, scraping up any browned bits from the bottom with a wooden spoon. Add the heavy cream and whole milk, stirring to combine. Bring to a gentle simmer over medium heat. The liquid should be steaming but not boiling—this prevents the cream from breaking and keeps the texture silky smooth.
Add the pasta shells to the simmering broth and return the cooked chicken to the pot. Stir gently and simmer for 10-12 minutes, stirring occasionally, until the pasta is tender but still has a slight bite and the flavors have melded together. Taste and adjust seasoning as needed.
Reduce heat to low and gradually stir in the freshly grated Parmesan cheese until completely melted and incorporated, then add the shredded mozzarella and stir until smooth and creamy. Keep the heat low during this step—high heat can make the cheese clumpy and separate rather than creating that luxurious, creamy texture. I always use freshly grated Parmesan for this dish because pre-grated versions have anti-caking agents that prevent it from melting as smoothly.
Remove from heat and stir in the fresh lemon juice to brighten the flavors. Ladle the chowder into bowls and top each serving with additional Parmesan cheese and chopped fresh parsley for a fresh, aromatic garnish.