Sauté the Shallot: Melt the butter in a medium saucepan over medium heat. Add the diced shallot and cook for 2–3 minutes, stirring often, until softened and fragrant.
Add Broth and Seasonings: Pour in the chicken broth and stir in the salt, pepper, and dried thyme. Bring the mixture to a gentle simmer.
Thicken the Gravy: In a small bowl, whisk together the cornstarch and 2–3 tablespoons of water to make a smooth slurry. Slowly pour the slurry into the simmering broth while whisking continuously.
Simmer Until Thickened: Continue simmering for 5 minutes, whisking often, until the gravy thickens to your desired consistency. Taste and adjust salt or pepper if needed.
Serve: Remove from heat and serve warm over chicken, mashed potatoes, or vegetables.