Preheat the oven to 375 degrees F. Slice off about ¼ inch from the top of the garlic. Place on a sheet of foil and drizzle with olive oil. Wrap in the foil, place on a baking sheet and roast until the garlic is soft, 50 to 60 minutes. Meanwhile, spread 1 cup parmesan in a thin layer on a baking sheet (use a silicone mat if you have one); sprinkle with the chopped rosemary. Bake until golden and bubbling, 5 to 6 minutes. Let cool on the baking sheet.
Meanwhile, rinse the potatoes well with cold water to get rid of any excess starch. Transfer the potatoes to a saucepan; cover with cold water by 1 inch, season generously with salt and bring to a boil. Reduce the heat to medium low and simmer, uncovered, until the potatoes are very tender but not falling apart, about 30 minutes.
Let the garlic cool slightly, then unwrap and squeeze the cloves out of the skins into a small saucepan. Add the milk and rosemary sprig. Heat over medium heat, stirring occasionally, until hot but not boiling. Reduce the heat to low and keep warm.
Drain the potatoes and return to the pot over low heat; cook until any excess water evaporates, about 2 minutes. Strain the milk mixture into the pot with the potatoes, pressing on the solids. Add the butter, olive oil and 2 teaspoons salt and mash well with a potato masher. Fold in the mascarpone and the remaining 1/4 cup parmesan.
Transfer the potatoes to a bowl; crumble the crispy parmesan on top before serving.