Preheat the oven to 425º F.
Crack the eggs into a medium mixing bowl. Add the milk and the salt. Whisk until the egg yolks and whites are well blended. Add the cheese, and give the mixture a quick whisk to blend. Set the mixture aside.
Heat the olive oil (until it shimmers) in a 12″ cast iron skillet or oven-safe non-stick skillet. Add the mushrooms and leeks. Simmer for 2-3 minutes, stirring occasionally, until semi-tender. Add the zucchini, and cook until they're tender—about another 2-3 minutes. Add the garlic and the kippers, stirring to incorporate them with the veggies. Simmer for another minute or so.
Give the eggs another quick whisk and carefully pour the mixture into the skillet, over the vegetables. Stir with a spatula to combine and distribute the mixture evenly across the skillet. Sprinkle the reserved cheese over the frittata, and let the frittata cook over the stove for about a minute to set the edges. (You'll see the edges slightly change color). Place the frittata in the oven, and bake for 7-10 minutes. When done, remove from the oven and let the frittata stand to cool for about 5 minutes before slicing into it.
Garnish with freshly chopped chives, slice into appropriate portions, and serve.