In a 12- by 15-inch baking pan, mix potatoes with 1/2 teaspoon olive oil; sprinkle with 1/2 teaspoon salt and mix to coat. Bake in a 400° regular or convection oven, stirring occasionally, until potatoes are browned and tender when pierced, 25 to 30 minutes.
Meanwhile, rinse fresh artichokes; trim off discolored stem ends. Break off and discard coarse outer leaves down to tender, pale green inner ones. Cut off thorny artichoke tips, pare coarse fibers from stems, and cut in half lengthwise. With a small, sharp knife, trim out fuzzy centers and discard (see notes).
In a 10- to 12-inch frying pan over medium-high heat, bring 1/2 cup water and the lemon juice to a boil. Add artichokes and 1/4 teaspoon salt; cover, reduce heat, and simmer until artichokes are tender when pierced, about 10 minutes (if using frozen artichoke hearts, skip step 2 and cook only 3 to 4 minutes). Uncover and boil, stirring often, until most of the liquid has evaporated.
In a large bowl, mix remaining 2 1/2 teaspoons olive oil, vinegar, and mustard. Add potatoes, artichokes (with any juices), frisee, capers, and tarragon. Mix gently to coat, and season to taste with salt and pepper. Serve warm.