Using the same skillet, add the diced shallot and minced garlic, sautéing until fragrant and softened. Pour in the white wine, deglazing the pan by scraping up any browned bits from the bottom. Stir in the orzo, ensuring it is evenly coated in the aromatic mixture, then add the chicken broth. Allow the orzo to simmer, stirring occasionally, until tender and fully absorbed, about 7 minutes.