Add 5cm of water in a medium saucepan that fits a metal steaming basket inside. Place potatoes in steamer and cook, covered, for 15 minutes, or until tender. Remove steamer from pot and leave on bench to dry out. Place in fridge (uncovered) or preheated oven to dry out up 20 minutes, if liked.
Preheat oven to 180C. Halve eggplants and score squares into flesh side, cutting almost through to the skin. Place skin-side down on baking paper-lined baking tray, toss with 1 teaspoon salt and olive oil to coat. Bake until very soft, about 25 minutes.
Meanwhile, mash potato with a potato masher or ricer, season with sea salt and freshly ground black pepper to taste.
When cool, scoop eggplant flesh into a large bowl and mash well with a fork. Add egg yolks and mix well until quite smooth. Add mashed potato and mix well to combine.
Add ½ cup flour to mixture and gently mix in, being careful not to overbeat. Add just enough flour to form a soft dough, adding a little more flour as needed. Gently fold in half the parmesan.
Turn dough out on to a floured surface, knead gently, adding a little more flour as needed to prevent sticky. (The dough should just hold together).
Divide dough into four and roll each quarter into a long thin log, about 2cm diameter.
Use a sharp knife to cut each rope diagonally into 2.5cm pieces. Use your thumb to roll each piece of gnocchi along the back of a fork so each piece has fork ridges along one side and a deep indent along the other. At this point you can transfer gnocchi to a baking sheet, freeze for 2 hours, then transfer to resealable snap-lock plastic bags in freezer for up to 2 weeks.
IHeat a large heavy-based frypan over a medium high heat, add 1-2 tablespoons rice bran oil and pan fry finger eggplant under golden and tender.
Half-fill a large saucepan with water and bring to boil, add large pinch salt. Add gnocchi, stirring gently until cooked, about 5 minutes. Gnocchi are cooked when they float. Drain into colander and transfer to serving plates.
In a large frypan, melt butter over medium heat, add sage leaves and fry until butter just begins to brown and sage crisps a little, about 3 minutes. Remove from heat, set aside.
Spoon sage burnt butter over gnocchi to serve, and toss through finger eggplant. Shave parmesan over the top using a vegetable peeler.