Reduce the pumpkin purée: Measure 1/2 cup 100% pure pumpkin purée into a small saucepan and place over medium-low heat. Spread it out into an even layer to maximize surface area. Cook for about 6-8 minutes, stirring often, until the purée reduces to a consistency similar to that of tomato paste. It should measure about 1/3 cup volume. Set aside to cool slightly.
Mix wet ingredients: Add 1/2 cup vegan butter, 1/2 packed cup brown sugar, and 1/4 cup granulated white sugar to a mixing bowl and stir to combine. Add in the reduced pumpkin purée and 2 teaspoons vanilla extract and stir to combine.
Add dry ingredients: Add in 1 1/3 cups all-purpose flour, 1/2 teaspoon baking soda, 1½ teaspoons pumpkin pie spice, 1 teaspoon ground cinnamon, 1/4 teaspoon ground ginger (optional), and 1/2 teaspoon fine salt. Mix until about 80% combined, then add in 1/2 cup vegan semisweet chocolate chips and fold them in to finish mixing the dough. The dough will be on the softer side at this point.
Portion and chill dough: Using a cookie scoop, divide dough into portions and transfer them to a plate or small baking sheet. (2 tbsp cookie scoop yields ~18 cookies. 3 tbsp cookie scoop yields ~12 cookies.) Put the plate in the fridge to allow the dough to chill for 30 minutes, or into the freezer to chill for 15 minutes. (You can chill the dough for up to 3 days, but please see notes.)
Preheat oven: Near the end of the chill time, preheat oven to 350°F with the rack in the center. Line a large cookie sheet with parchment or a silicone mat.
Finishing touches: Remove the chilled cookie dough portions from the fridge or freezer, and roll them smooth in your palms. Place them on the prepared cookie sheet with enough room to spread. Use the remaining 1/4 cup vegan chocolate chips to top your cookies, gently pressing a few chips into the top of each cookie dough ball.
Bake: Bake in the preheated oven until set in the center and lightly crisped around the edges. Smaller cookies (2 tbsp scoop): 10-12 minutes. Larger cookies (3 tbsp scoop): 12-15 minutes.
Cool and enjoy: Remove from oven and sprinkle with flaky salt if desired. Let the cookies rest on the cookie sheet for about 5 minutes to firm up, then transfer to a wire baking rack and enjoy.