Heat a large deep skillet or Dutch oven over medium-high heat and add 1 tablespoon of the olive oil.
Toss the cut chicken with 1 teaspoon Italian seasoning, 1 teaspoon paprika, and 1/2 teaspoon kosher salt. Add the chicken to the hot skillet and sauté, stirring occasionally, until golden and cooked through, 4 to 6 minutes; transfer to a plate.
Reduce heat to low, add the remaining 1 tablespoon oil to the pan, then add the diced shallot and 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 remaining 3/4 teaspoon kosher salt and cook, stirring, for about 30 seconds until fragrant.
Stir in the orzo and the cherry tomatoes and cook, stirring constantly, for 1 minute 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, about 12 to 14 minutes, stirring and scraping the bottom occasionally. Add splashes of broth if the orzo becomes too dry.
Stir in the Parmesan, chopped spinach, red pepper flakes, half of the sliced basil, and the reserved chicken. Cook, stirring, until the spinach just wilts, about 1 minute. Taste and adjust seasoning if needed.
Serve hot, sprinkled with the remaining basil and additional Parmesan if desired.