Bring a large pot of water to boil. Add salt generously. Add potatoes and boil until just fork tender (anywhere from 10-20 minutes, depending on the size of your potatoes).
Meanwhile, Add olive oil to a saucepan and heat over low heat for 10-15 minutes, or until just fragrant. Remove from heat. Strain out rosemary and discard. Set infused oil aside.
Preheat oven to 425F. Prepare a baking sheet by brushing a layer of your rosemary oil all over the bottom of the pan.
When your potatoes are tender, drain well and allow to cool a few minutes. Spread potatoes out on oiled baking sheet, allowing a couple of inches in between. Using the back of a fork, gently press down on the potatoes, until they burst. Continue until all the potatoes are smashed. Brush liberally with rosemary oil and sprinkle with a little coarse salt.
Roast in preheated oven for about 15 minutes, then remove and brush again with olive oil. Return to oven and roast until golden brown on the bottom and sides, about 10 minutes longer for really small potatoes, up to 20 minutes longer if they are a bit larger.
If you'd like your potatoes crispier, pop them under a hot broiler for a few minutes.
Remove from oven and give one final brush with rosemary oil, then sprinkle with a bit more coarse salt.