Heat the oven to 375℉.
Melt 3 tablespoons of the butter in a small pan over medium heat. Add the onions and cook until soft. Add the garlic, and cook for another minute. Place in a bowl to cool for a few minutes, then add the spinach, cheeses, parsley, a grating of nutmeg, ½ teaspoon of salt and a few grindings of pepper. Mix well, then taste and adjust the seasonings to your liking. Add the eggs and mix thoroughly.
Melt the remaining butter. Line a cookie sheet with parchment paper, and brush it with butter.
Remove the phyllo from its package, cut across the roll into 3 or 4 even sections, and cover with a towel. Unroll 1 cut section into a strip, and brush the top phyllo sheet with a little butter. Place a teaspoonful of filling at one corner of the strip. Using 2 sheets of dough, fold it over the filling at a right angle, forming a triangle. Then fold in the other direction, as if folding a flag. Keep folding until you reach the end of the dough. Brush the top with butter and place on the baking sheet. Repeat with the other pieces of dough.
Bake until golden brown, 15-20 minutes. Allow to cool for 5-10 minutes before serving.
To make ahead: Unbaked spanakopita triangles freeze well. Bake from frozen until golden brown.