Combine the cream cheese, Greek yogurt, sugar and vanilla. Whisk together well and set aside.
Cut the pear into thin slices.
Preheat a pan on medium-high heat. You will have to work fast here: add the butter and let it brown (it will only take a couple of seconds.) Add the brown sugar and rum. Stir constantly. Add the pear slices and stir until the slices a coated. Cook the pears, stirring often, until caramelized.
Prepheat the oven to 400.
Divide the cream filling between the four pastry squares.
Twist the edges of the pastry up to form circles. (Just the edges.)
Divide the caramelized pears between the pastries as well.
Brush the edges of the pastry with some melted butter.
Bake for 12-15 minutes, until the pastry is raised and golden. (Don't worry, the pastry will puff in the center but it will go down once you take it out of the oven.)