Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the finely diced 1/2 white onion and sauté until softened, about 3–4 minutes; add the minced garlic for the last minute and cook until fragrant.
Stir in 1 cup chicken broth, 3/4 cup uncooked orzo, the 14.5-ounce can of undrained diced tomatoes, 1 teaspoon Italian seasonings, 1/2 teaspoon kosher salt, and 1/4 teaspoon crushed red pepper flakes.
Bring the mixture to a boil, then reduce heat to a simmer. Cover and cook 12–15 minutes, stirring once or twice, until the orzo is tender and most of the liquid is absorbed.
Add 2 cups shredded rotisserie chicken and 3 cups chopped spinach to the skillet for the last 3 minutes of cooking; stir until the spinach wilts and the chicken is heated through.
Remove from heat, sprinkle with 1/4 cup grated Parmesan cheese, stir to combine, adjust salt to taste, and serve.