Cover potatoes with cold water in a large pot and add 1 tbsp salt. Boil until almost tender, 10 to 15 minutes. Drain potatoes and let cool slightly. Transfer to a cutting board and lightly crush to about 3/4 inch thick with a mallet, keeping potatoes intact as much as possible.

Heat olive oil in a large skillet over medium-high heat. Transfer potatoes to skillet, and add the garlic, shallots, lemon zest and red pepper flakes. Lower heat after 2 minutes to medium low and continue to cook for 10-15 minutes more until the shallots and garlic are tender.

Season the pan fried smashed potatoes with salt and pepper to taste and sprinkle tarragon leaves on top.