Preheat oven to 450 degrees with rack in the middle of the oven.

Brush a large baking sheet with oil.

Microwave potato on high under tender, about 12 minutes. You need 2/3 cup packed mashed potato. Just scoop the potato into a bowl and mash well and let cool. No need to add butter or milk to the potato.

Combine flour, half the rosemary and 1 tsp salt. Add potato and mix to blend.

In a small bowl combine the sugar, water and yeast. Let stand till foamy, about 5 minutes. Stir in 3 tbsp olive oil.

Pour yeast mixture into the flour and mix until smooth - about 1 minute. Scxrape dough onto a lightly floured surface and knead until silky, sprinkling more flour as needed. The gluten in foccacia sould not be developed, so knead for 1 minute or less. Place in a large oiled bow, turning to coat top, cover with plastic wrap and let rise until doubled, about 1 hour.

Punch down dough and knead for 30 seconds on a lightly floured surface. Stretch or pat dough to a 12-in round. Transfer round to baking sheet and press all over with finertips to make dimples. Brush with 1 tbsp oil. Press olive halves, cut side down, into dough (These are optional). Sprinkle with sea salt. Cover with a cloth and let rise until just puffy, about 20 minutes. Bake until golden, about 18 minutes.