Pat chicken dry and transfer to a large bowl. Add Italian seasoning; season with salt and pepper. Sprinkle flour over chicken and toss to coat.

In a large skillet over medium-high heat, heat 1 Tbsp. oil, then melt 1 Tbsp. butter. Add half of chicken and cook, turning occasionally, until golden brown, 2 to 3 minutes per side. Transfer to a plate. Repeat with 1 Tbsp. oil and remaining chicken.

In same skillet over medium heat, heat 1 Tbsp. oil. Add mushrooms and cook, stirring occasionally, until softened, about 5 minutes.

Add shallots and remaining 1 Tbsp. oil; season with salt. Cook, stirring frequently, until translucent, about 2 minutes. Add garlic and thyme and cook, stirring, until fragrant, about 1 minute. Add orzo and remaining 1 Tbsp. butter and cook, tossing frequently, until orzo is coated, 2 to 3 minutes. Add wine and cook, stirring occasionally and scraping browned bits from bottom of pan, until slightly reduced, 2 to 3 minutes.

Add broth and increase heat to high. Bring to a boil, then reduce heat to medium. Simmer, stirring occasionally, until thickened and flavors have melded, about 7 minutes. Add cream and cook, stirring frequently, until orzo is creamy, about 2 minutes more.

Return chicken to pan and toss to combine; season with salt, if needed. Top with parsley.