Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, 8 to 10 minutes.

In a medium bowl, stir together the bread crumbs, parsley, eggs, milk, ketchup, Romano cheese, salt, and pepper. Add the chicken and combine well. Using a melon baller (or a teaspoon measure) to scoop up the mixture, roll the seasoned chicken into ¾-inch mini meatballs.

Heat the oil in a large skillet over medium-high heat. Working in batches, add the meatballs and cook without moving until brown on the bottom, about 2 minutes. Turn the meatballs and brown the tops, about 2 minutes longer. Add the chicken broth and tomatoes and bring to a boil, using a wooden spoon to scrape up the brown bits that cling to the bottom of the pan. Reduce the heat to low and simmer until the tomatoes are soft and the meatballs are cooked through, about 5 minutes.

Drain the pasta, reserving about 1 cup of the pasta water. Transfer the pasta to a large serving bowl and add ½ cup of the Parmesan. Toss to coat the orecchiette lightly, adding some of the reserved pasta water to help make a sauce. Add the meatball mixture, bocconcini, and ½ cup of the basil and combine. Garnish with the remaining ½ cup of Parmesan and the remaining basil.