Cut dark green leaves from leeks and discard or save for cooking stock later. Rinse stems (light green and white portion of stalk) and chop into thin discs. Wash discs in water second time to remove any remaining dirt. Dice onion and garlic. Cube potatoes.
Melt butter on high heat in pot, add leeks, onion, and garlic. Stir, allowing vegetables to lightly caramelize.
In small container, combine 2 tbsp flour to 1/2 cup of the broth. Stir to dissolve flour. Add to pot along with remaining broth. Bring contents of pot to boil stirring constantly.
Add potatoes, salt and pepper to taste, cover, and simmer for 30 minutes or until potatoes are finished.