Pat the pumpkin puree dry on paper towels to remove excess moisture. Set aside.
Make the cream cheese filling: Beat together the vegan cream cheese, brown sugar, and cornstarch with a hand mixer until smooth. Scoop 11–13 small teaspoon-sized portions onto a parchment-lined baking sheet. Freeze for 15–20 minutes until firm.
Make the cookie dough: In a large bowl, cream together the vegan butter, granulated sugar, brown sugar, pumpkin puree, dairy-free yogurt, and vanilla extract with a hand mixer. Add the pumpkin pie spice, baking soda, and sea salt and mix again. Fold in the flour with a silicone spatula until just combined.
Refrigerate the cookie dough for 10–20 minutes. While it chills, preheat the oven to 350°F (175°C) and whisk together the sugar and pumpkin spice coating in a small bowl.
Shape the cookies: Scoop one ball of dough (about 1.5 tablespoons) and press flat in your palm. Place one frozen cream cheese portion in the center. Fold the dough edges up and around the filling and roll into a smooth sealed ball. Roll in the pumpkin spice sugar coating. Place on a parchment-lined baking sheet. Repeat with remaining dough.
Bake for 11–14 minutes until edges are lightly golden. Immediately reshape edges if needed. Cool on the baking sheet for 10–15 minutes before serving.