Preheat the oven to 425 degrees F (220 degrees C). Fit pie crust into a 9-inch pie dish and place it on a baking sheet.
Combine pumpkin puree, condensed milk, eggs, pumpkin pie spice, and a pinch of salt in a large bowl; mix until combined. Pour into the pie crust, leaving a bit of room at the top.
Combine cream cheese, granulated sugar, espresso powder, egg yolk, vanilla, and a pinch of salt in a medium bowl; whisk until combined and smooth.
Dollop the cream cheese mixture over the pumpkin pie filling then use a toothpick or thin knife to swirl the cream cheese into the pumpkin.
Bake in the preheated oven for 15 minutes. Reduce heat to 350 degrees F (175 degrees C) and continue to bake until filling is set, 35 to 40 minutes. Remove from the oven, set on a wire rack, and cool completely before serving.