Preheat the oven to 400 degrees F.
Unwrap the phyllo and remove 5 sheets from the stack. Reserve the remaining dough for another use.
Put a round baking pan on top of the phyllo sheets and trim the sides. Lay the phyllo circles flat between 2 damp kitchen towels. Set the pan aside.
Lay down 1 piece of phyllo dough on your work surface. Brush with butter and sprinkle with ground pistachios. Put a second phyllo sheet on top of the first and brush with butter and sprinkle with pistachios. Repeat 3 times, making 5 layers and the top being only phyllo. Put the stacked dough into the baking pan. Alternately, cut into squares 2 inches larger than muffin cup size; lightly butter the muffin tin and gently press prepared phyllo squares into each muffin cup to form small bowl shapes.
Bake for about 14 to 16 minutes, until golden brown and crisp. Remove the pan from the oven and allow the tart to cool completely before topping.
Crumble goat cheese over the crust. Top with tomatoes and season with salt and pepper, to taste. Slice and serve.