Put the potatoes in a large pot and add water to cover by 3 inches. Season the water with salt. Bring to a boil over medium-high heat, reduce the heat to medium-low and simmer until the potatoes are tender when pierced with a fork, about 10 minutes. Drain well in a colander. Transfer the potatoes to a towel-lined baking sheet and let cool. Using the smooth side of a meat tenderizer, carefully smash each potato to about 1/2-inch thickness.
Preheat an oven to 200ºF. Set a wire rack on a baking sheet.
In a square stainless-steel griddle pan over medium-high heat, warm the 1/4 cup olive oil. Add the rosemary sprig and fry until crispy, about 2 minutes. Transfer to a bowl.
Working in batches and adding more olive oil to the griddle pan as needed, sear the smashed potatoes, turning once, until well browned and crispy, about 3 minutes per side; add 1/2 to 1 Tbs. butter during the last 1 minute of cooking. Transfer the potatoes to the rack-lined baking sheet and season with salt and pepper. Place in the oven to keep warm.
To serve, transfer the potatoes to a warmed serving bowl. Top with the chopped rosemary, thyme and parsley and garnish with the fried rosemary sprig. Serve immediately. Serves 10 to 12.
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