For the Pie Crust:

1. Combine the flour and salt in a food processor. Scatter the butter over the flour and quickly pulse several times just to submerge the butter. Mix the half-and-half and vinegar together, pour in, and pulse several more times until the liquid is combined.
2. Dump the mixture out onto a floured surface and pat into a fat disk. Wrap in plastic and refrigerate at least 30 minutes.
3. Roll out the dough on a floured surface into a thin round an inch or so larger than the 9-inch pie plate. Arrange the crust in the plate, avoiding stretching it. Crimp the edge decoratively. Refrigerate the crust.

For the Pie Filling:

1. Combine in a food processor the pumpkin puree, brown sugar, goat cheese, egg and yolk, vanilla, and spices, process until well blended. Through the feed tube, slowly add the butter and half-and-half until mixed thoroughly.
2. Pour the filling into the chilled pie shell. Brush the edges with the beaten egg.
3. Preheat the oven to 350 degrees. Bake the pie for 15 minutes, then turn the oven down to 300 degrees and bake for 45 minutes, or until the filling looks set. Turn off the oven and let the pie sit inside for 5 minutes. Allow to cool at room temperature.
4. Refrigerate covered for at least 1 hour.

For the Caramel-Pecan Topping:

1. Place 3 tbsp of water in a heavy saucepan. Sprinkle sugar into the middle of the pan and top it with the agave syrup, salt, and vanilla. Cook over medium-high heat until the mixture melts into a golden-brown caramel and has a glossy sheen. Do not stir, but swirl if it melts unevenly.
2. Remove from the heat and whisk in the remaining 3 tbsp water, followed by the vanilla extract and butter. Return the mixture to medium-high heat. Pour in the cream and whisk 5-8 minutes, until you have moderately thick caramel sauce with very small bubbles. Stir in pecans and let cool briefly.
3. Spread mixture evenly over chilled pie. Refrigerate again until set, then serve.