Season chicken all over with 3/4 teaspoon salt and the black pepper. Heat olive oil in a large deep skillet over medium-high heat until shimmering. Add chicken in a single layer and cook until deeply golden brown, 5 to 6 minutes per side. The chicken does not need to be cooked through. Transfer to a plate.

Reduce heat to medium. Add shallot to the skillet and cook, scraping up any browned bits, until softened, about 2 minutes. Add garlic and cook until fragrant, about 30 seconds. Stir in sun-dried tomatoes, oregano, red pepper flakes if using, and remaining 1/4 teaspoon salt. Cook for 1 minute to bloom the spices.

Add orzo to the skillet and stir constantly until the grains are lightly toasted at the edges and smell nutty, about 2 minutes. This prevents mushy orzo and adds depth.

Pour in warm chicken broth and stir well, making sure no orzo is stuck to the bottom. Nestle the seared chicken and any accumulated juices into the orzo. Bring to a gentle boil, then reduce heat to low, cover, and simmer for 12 to 14 minutes until orzo is tender and chicken registers 165°F internally. Stir once halfway through to prevent sticking.

Remove from heat. Stir in heavy cream and Parmesan until the sauce is silky and coats the orzo. Let rest uncovered for 3 minutes to thicken slightly. Taste and adjust salt if needed. Serve topped with torn basil and extra Parmesan.