Heat a large deep skillet or Dutch oven over medium-high heat and add 1 tablespoon of the olive oil.
Toss the chicken pieces with 1 teaspoon Italian seasoning, 1 teaspoon paprika, and 1/2 teaspoon kosher salt. Add the chicken to the hot pan and sauté, stirring occasionally, until golden and cooked through, 4 to 6 minutes. Transfer the chicken to a plate.
Lower the heat to medium-low, add the remaining 1 tablespoon oil, then add the diced shallot. Cook, stirring often, until softened, about 3 minutes.
Add the minced garlic, ground black pepper, the remaining 1 teaspoon Italian seasoning, remaining 1 teaspoon paprika, and the remaining 3/4 teaspoon kosher salt. Cook and stir for 30 seconds until fragrant.
Stir in the orzo and the cherry tomatoes and cook for 1 minute, stirring constantly, to coat and lightly toast the orzo.
Pour in the chicken broth and increase heat to bring to a gentle boil, stirring frequently and scraping the bottom to prevent sticking. Cover, reduce heat to medium, and cook until most liquid is absorbed and orzo is al dente, 12 to 14 minutes, stirring occasionally and adding splashes of broth if it becomes too dry.
Stir in the Parmesan, baby spinach, red pepper flakes, half of the sliced basil, and the reserved chicken. Continue stirring until the spinach is just wilted, about 1 minute.
Taste and adjust seasoning with additional salt, pepper, or red pepper flakes as desired. Serve hot topped with remaining basil and extra Parmesan.
