Spread chopped hazelnuts in a single layer on a baking sheet. Bake in the preheated oven for 5 to 10 minutes, stirring once or twice, and watching very carefully as they will burn very easily. Remove from the oven when browned and fragrant.
Cut baby carrots in half cross-wise. In a saucepan over medium heat, bring water, carrots, salt, and 1 tablespoon of butter. Bring to a boil, and reduce heat to low. Cover, and simmer very lightly for 10 to 15 minutes, or until tender but firm. Drain and set aside.
Return pan to the stove over medium heat, and melt the remaining 2 tablespoons of butter. Cook shallots in the melted butter, stirring occasionally, until translucent. Add Marsala and sugar, and stir continually until sugar is completely dissolved. Continue simmering until sauce has thickened slightly.
Once thickened, toss carrots and hazelnuts with the sauce until well coated. Garnish with parsley, if desired. Serve immediately.