Lay fillets skin side down in a 9x13-inch glass baking dish. In a small bowl, combine brown sugar, salt and peppercorns and sprinkle evenly over fillets. Mix together beets and orange zest and sprinkle evenly over sugar-salt mixture. Sprinkle vodka over beet-zest mixture, arrange dill over top, cover with plastic wrap, and refrigerate for 8 hours or overnight.
When ready to serve, scrape off dill and beet mixture and pat dry with paper towel. With skin side down, slice crosswise across fillet in very thin slices (discard skin).
On the large holes of a box grater, grate potatoes into a large bowl. Stir in salt and let sit for 2 minutes. Squeeze out excess liquid and shape potatoes into small mounds, (about 1 heaping tablespoon for bite sized appetizers).
In a large skillet over medium low heat, heat oil and melt butter. Add potato cakes in batches (do not overcrowd pan), and using a metal spatula, gently press cakes down unti ¼ inch thick. Cook, turning once, until golden, about 5 minutes per side. Transfer rosti to a paper towel lined tray. Season lightly with salt. Repeat with remaining cakes until done.
Prepare Mimosa Eggs: Push hard boiled eggs one at a time through a fine metal sieve. Set aside.
Arrange one slice of cured trout on each rosti. Top with a dollop of crème fraiche, trout roe, chopped chives and egg garnish. Serve immediately.
Nutrients per Serving: Calories 177 Fat 9g Saturated Fat 3 g Trans Fat 0.1g Sodium 701mg Carbohydrate 15g Fibre 1g Sugars 1g Protein 11g