Make the dough: Beat the butter and cream cheese in a large bowl with a mixer on medium-high speed until creamy, about 5 minutes. Reduce the mixer speed to low and beat in the confectioners? sugar and salt until fluffy, about 1 more minute. Gradually beat in the flour until the dough comes together.
Turn out the dough onto a floured surface and knead a few times until smooth. Divide the dough in half and roll each half into a 12-inch-long rope. Cut each rope into 12 pieces. Roll the pieces into balls and put the balls in a 24-cup mini-muffin tin. Use your thumb to press the dough into the bottom and up the sides of the cups, making the bottom slightly thinner than the sides. Refrigerate until firm, about 1 hour.
Meanwhile, make the filling: Toss the apples, lemon juice, granulated sugar, apple pie spice and vanilla in a medium bowl. Melt the butter in a medium skillet over medium heat. Add the apple mixture and stir to coat. Cover and cook, stirring occasionally, until tender, about 20 minutes. There should be some liquid left in the skillet; if not, stir in 1/4 cup water.
Mix the cornstarch and 1 teaspoon water in a small bowl; stir into the apple mixture and bring to a boil. Cook until thick and bubbling, 30 seconds to 1 minute. Transfer to a bowl to cool, about 20 minutes.
Preheat the oven to 350 degrees F. Divide the apple mixture evenly among the muffin cups. Bake, rotating the pan halfway through, until the tassies are golden, about 30 minutes. Let cool 5 minutes in the pan, then use an offset spatula to remove the tassies and transfer to a rack to cool completely. They will crisp as they cool.