Preheat the oven to 350°F. Lightly grease a donut pan with softened butter or cooking spray and set aside.
In a large mixing bowl, whisk together the oil, eggs, sugars, and pumpkin until smooth. In a separate bowl, whisk together the flour, baking powder, spices, and salt.
Tip the flour mixture into the pumpkin mixture and stir until smooth and thoroughly combined.
Fill the wells of the donut pan about ¾ of the way full with the donut batter.* Bake for 14 to 16 minutes, or until a toothpick inserted into the donuts comes out clean. Cool on a wire rack for a few minutes before popping out the donuts. Repeat with any remaining batter.
Salted Caramel Sauce
Place the sugar, syrup, and water in a small saucepan over high heat. Bring the sugar mixture to a boil and cook without stirring until the mixture turns a medium amber color.
Once it reaches the correct color, remove from the heat. Slowly (and carefully) whisk in the cream (the mixture will bubble up a bit, so use caution).
Whisk in the butter until melted. Transfer the caramel to a heat-safe container and stir in the salt and vanilla. Let cool until thickened.
Salted Caramel Glaze
Stir all of the ingredients together until combined and smooth. The glaze should be thick enough to cling to the donuts without running off, but thin enough that it settles smoothly on the top.
Add more milk until the correct consistency is achieved (around the same consistency of honey or slightly thicker).