Mix the kasha and egg white together in a small bowl until the kasha is well coated.
Heat a large nonstick skillet over medium-high heat.
Add the kasha mixture and cook, stirring constantly, until the grains soften and separate and the egg adheres to the grains and dries out, about 3 minutes.
Let cool completely.
Spread the hazelnuts out on to a baking sheet and bake until golden and toasted, 8 to 10 minutes.
Transfer to a cutting board and cool.
Rub the skins off the nuts with a kitchen towel, then coarsely chop the nuts.
Bring 2 cups of water to a boil in a medium saucepan.
Add the kasha, bring back to a boil, reduce the heat to medium low, cover and simmer until most of the water is absorbed and the kasha is tender, about 15 minutes.
Spread the grains out on a baking sheet to cool.
Whisk together the vinegar, oil, honey and 3/4 teaspoon salt in a large bowl.
Add the cooled kasha, hazelnuts, carrot, parsley and feta and gently stir to combine.