Place potatoes in one layer in a large saucepan. Add cold water to cover by at least an inch. Add 1 t. salt and bring water to boil. Reduce heat and simmer until potatoes are cooked, about 25-30 minutes.
Drain thoroughly, then wrap loosely in a tea towel to draw out excess moisture. Remove tea towel and place potatoes in one layer on parchment paper covered baking sheet. Cover your hand with a tea towel(for protection) and press down on each potato to "smash" it lightly.
Cover with plastic wrap and refrigerate to cool completely. Dish can be prepared to this point; cover and refrigerate.
Preheat oven to 450°F If chilled, bring potatoes to room temp(about 20 minutes). Pour olive oil generously over potatoes and sprinkle with remaining 2 t. salt. Lift potatoes slightly to ensure they're well coated with oil underneath.
Roast potatoes until brown and crispy, about 30 minutes. Serve immediately.