Trim leeks, discarding dark green part, and halve lengthwise. Cut leeks crosswise into 1/2-inch-thick slices and in a large bowl of cold water wash well. Drain leeks.
In a 12-inch heavy ovenproof skillet cook leeks and onions in oil over moderate heat, stirring, until softened, about 15 minutes. Add garlic and cook, stirring, 1 minute. Add flour and cook, stirring, 3 minutes. Add broth in a stream, stirring, and simmer, stirring, until thickened, about 3 minutes. Stir in lemon juice and salt and pepper to taste and remove skillet from heat.
Preheat oven to 400°F.
Peel potatoes and halve lengthwise. Arrange each potato flat side down and make crosswise slices about 1/4 inch apart, cutting down to about 1/4 inch from flat side but not all the way through (a metal skewer inserted lengthwise about 1/4 inch from flat side will prevent slicing all the way through). Remove skewer if using.
Arrange potato halves, flat sides down, in leek mixture and bring mixture to a simmer. Brush potatoes with butter and sprinkle with paprika and salt and pepper to taste. Bake mixture in lower third of oven 1 hour and 15 minutes, or until potatoes are tender within and crisp and golden on top.
