In a 2- to 3-quart pan, bring broth to a boil over high heat.
Add peas; cover and simmer until peas are tender to bite, about 12 minutes.
Drain peas and let cool.
In a bowl, stir peas with ham, oil, vinegar, tarragon, and sugar; add salt and pepper to taste.
Spoon pea mixture on lettuce-lined salad plates.