Cook leeks, onions, and shallots, in oil, in a pot for 2 to 3 minutes. Lower heat to medium-low and slowly cook 20 to 25 minutes or until vegetables are lightly browned. Whisk in flour and cook over medium heat 1 to 2 minutes.
Mix in broth, thyme, salt, and pepper and bring to a boil. Continue boiling, whisking continually 1 to 2 minutes or until thick.