Spinach and Goat Cheese Tartlets

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4 tablespoons unsalted butter

3 sheets frozen phyllo dough, thawed

2 tablespoons grated parmesan cheese

Vegetable oil, for brushing

1 large shallot, minced

1 clove garlic, minced

1 teaspoon all-purpose flour

1/4 cup milk

Pinch of freshly grated nutmeg

Kosher salt and freshly ground pepper

3 1/2 ounces mild goat cheese, softened

2 teaspoons finely grated lemon zest

1 tablespoon white wine vinegar

2 large eggs, separated

1 10-ounce box frozen chopped spinach, thawed and squeezed dry

Chopped chives, for garnish