Preheat the oven to 350 degrees F. Brush the cups of a 12-cup muffin tin with 1 tablespoon of the melted butter.
On a clean work surface, lay out your first sheet of phyllo pastry. Gently brush it all over with 1 tablespoon of the melted butter. Place the second sheet on top and brush with 1 more tablespoon of the melted butter. Continue in this method until all four sheets have been used, making sure to brush the top of the fourth sheet with the remaining 1 tablespoon of melted butter. Using a pizza cutter or a sharp knife, cut the layered phyllo sheet into 12 squares. If the phyllo sheet is portrait oriented to you, cut it into three columns lengthwise and 4 rows across (just like the cupcake tin).
Line each cup with a square of the phyllo and crack an egg into each phyllo-lined cup. Top each egg with a wedge of cheese and a small piece of ham. Sprinkle about 1/8 teaspoon of the herbes de provence over each tart.
Bake until the phyllo dough is golden brown and the whites of the eggs are set, about 15 minutes. If you like your egg yolk fully cooked, be sure to bake your tarts for a couple more minutes.
Remove from the oven and allow to cool for 5 – 10 minutes. Carefully lift each tart from the tin with a small spatula and enjoy warm or at room temperature.