Place potatoes in a large pot and cover with cold water by at least 1 inch. Add 1 tablespoon of salt.
Bring to a boil, then reduce heat and simmer for 15 to 20 minutes until fork-tender.
Drain the potatoes and let them sit in the colander for 5 minutes to steam dry.
Preheat oven to 425°F (220°C) and lightly grease a large rimmed baking sheet with olive oil.
Arrange potatoes on the baking sheet. Use a heavy flat-bottomed glass or a potato masher to gently press each potato down until it is approximately 1/2 inch thick.
Drizzle the smashed potatoes with the olive oil and sprinkle with kosher salt, black pepper, minced garlic, and rosemary.
Roast for 25 to 30 minutes, flipping once halfway through, until the edges are golden brown and crispy.
Remove from the oven and serve immediately.