Add potatoes to a large pot of salted cold water. Bring water to a simmer and cook until tender, about 15-20 minutes.
Strain potatoes and add to a large bowl. Use a potato ricer for smooth potatoes or a hand masher for more textured potatoes.
Mix in olive oil, half and half, salt, and parmesan. Careful not to overmix to avoid a gluey texture.
Top with chives and serve.
For smooth potatoes use a hand ricer to push cooked potatoes through before adding in the other ingredients. Otherwise use a hand mashed for a more rustic texture.