How to Make It
Preheat the oven to 375°. In a small bowl, combine the melted butter and olive oil. Lightly brush two 12-cup mini-muffin tins with a little of the butter-oil mixture. Lay a sheet of phyllo dough on a work surface and brush lightly with a little of the butter-oil mixture. Top with the remaining 2 sheets of phyllo brushed with the butter-oil mixture.
Using a 2 1/4 -inch round biscuit cutter, cut out 24 phyllo rounds. Press the rounds, buttered side up, into the muffin cups. Bake for about 4 minutes, or until golden and crisp; don't let the phyllo burn. Let the phyllo cups cool slightly, then carefully transfer to a rack to cool completely.
Melt the remaining 1 teaspoon of butter in a large skillet. Add the leeks and a large pinch of salt and pepper. Cook over moderate heat, stirring, until tender but still slightly green, 8 to 10 minutes.
Just before serving, spoon the sautéed leeks into the phyllo cups. Top each cup with a piece of smoked salmon and serve immediately.