Melt butter in a 12 to 14-inch frying pan over low heat.
Add pine nuts and cook, stirring, until golden (about 1 minute).
Lift out nuts with a slotted spoon and set aside on paper towels to drain.
Increase heat to medium.
Add onions to pan; cook, stirring occasionally, until soft.
Meanwhile, trim and discard ends and tops from leeks, leaving about 3 inches of green leaves.
Discard tough outer leaves.
Split leeks lengthwise; rinse well, then thinly slice crosswise (you should have 9 cups).
Add leeks, garlic, and tarragon to pan.
Continue to cook, stirring occasionally, until leeks are very soft (about 15 more minutes).
Add lemon peel, lemon juice, and pine nuts; season to taste with salt.