Put a rimmed baking sheet in the lower third of the oven and preheat to 425 degrees F. Toss the potatoes and shallots with 2 tablespoons olive oil, 1/4 teaspoon salt and a few grinds of pepper. Spread on the hot baking sheet and roast, tossing halfway through, until tender and golden, 25 to 30 minutes. Let cool.
Meanwhile, bring a medium saucepan of salted water to a boil. Add the snap peas and cook until bright green but still crisp, 1 to 2 minutes. Transfer to a bowl of ice water; let cool. Drain and pat dry.
Whisk the vinegar, mustard, honey, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Slowly whisk in the remaining 1/4 cup olive oil. Add the roasted potatoes and shallots, peas, tomatoes, cucumbers, radishes, parsley, chives and tarragon. Season with salt and pepper and toss.