1. Place potatoes in a large pot, cover with cold water by 2 inches and bring to a boil; add salt. Simmer until fork-tender but not falling apart, about 30 minutes; drain.
2. Transfer potatoes to a large mixer bowl and, using whisk attachment, beat on medium speed until finely crumbled. Add milk, extra-virgin olive oil, and 2 teaspoons salt; beat until just smooth, adding more milk as needed for a light, creamy texture.
3. Stir in kalamata olives and fresh thyme. Makes 8 to 10 servings.