Heat butter in a medium saucepan over medium heat. Add shallot, carrot(s) and celery and cook 5 minutes, stirring occasionally.
Add quinoa to saucepan and cook, stirring, 1 minute. Pour in broth plus 1/4 cup water. Stir in thyme and salt.
Bring to a boil over medium-high heat. Cover; reduce heat to medium-low and cook until liquid is absorbed, about 20 minutes. Serve warm.