Preheat the oven to 350°F.
Place the gingersnap cookies and brown sugar in a food processor. Pulse until the cookies are reduced to coarse crumbs.
Add the ground ginger and cinnamon, then pulse once or twice more to distribute the spices evenly.
Pour in the melted, slightly cooled butter and process briefly until the crumbs are thoroughly moistened.
Transfer the crust mixture to an ungreased 9-inch pie plate or divide it between two 7½-inch tart pans fitted with removable bottoms.
Using your fingertips, spread and gently press the crumbs evenly across the base and up the sides of the pan.
Compact the crust firmly with the flat bottom of a measuring cup or drinking glass.
Bake for 5–8 minutes. Remove the crust from the oven and allow it to cool for at least 10 minutes before adding the filling.
Combine the pumpkin purée, granulated sugar, brown sugar, fresh ginger, cinnamon, cloves, and sea salt in a large, heavy-bottomed saucepan.
Cook over medium heat until the pumpkin mixture begins to sputter.
Continue cooking for 5 minutes, stirring frequently, until the mixture develops a smooth, glossy consistency.
Remove the saucepan from the heat. Gradually add the sweetened condensed milk while whisking continuously until completely incorporated.
Whisk in the whole eggs and egg yolk individually, making certain each addition is fully blended before adding the next.
Add the vanilla extract and stir until evenly combined.
Bake at 350°F for 30 minutes, or until the outer edges of the filling are beginning to set.
Lower the oven temperature to 325°F and continue baking for another 25–35 minutes. The filling should be largely set while retaining a slight jiggle in the center.
If the crust becomes too dark before the filling has finished baking, protect its edges with aluminum foil or a pie-crust shield.
The pumpkin filling may puff or develop small bubbles while it bakes. This is normal and will subside as the pie cools.
Transfer the finished pie to a wire cooling rack and leave it undisturbed for 2–3 hours, allowing the filling to cool completely and become fully set.
The residual heat will continue to cook and firm the center during the cooling period.
Serve the pie at room temperature or chilled, garnished with freshly whipped cream if desired.