Preheat the oven to 375°F. Spray a 9-inch loaf pan with nonstick cooking spray and line with parchment paper.
Combine the flour, sugar, cinnamon, baking soda, and salt in the bowl of an electric mixer on low speed. Add the vegetable oil and pumpkin purée and blend until fully combined. Add the eggs, one at a time, blending well after each addition.
Pour the batter into the prepared pan and smooth the top. Bake for 1 to 1½ hours, until a cake tester comes out clean. Remove from the oven and let cool for 30 minutes. Invert the cake onto a wire rack and let cool completely.
Beat the butter, cream cheese, vanilla extract, and salt in the bowl of an electric mixer on medium speed for about 2 minutes, until light and fluffy. With the mixer on low speed, add the powdered sugar, a little at a time, blending until creamy. Stir in the pecans. Set the icing aside.
Cut the loaf of pumpkin cake into 8 even slices. Whisk together the eggs, milk, cinnamon, and salt in a shallow baking dish. Soak the cake slices in one layer in the custard for 1 to 2 minutes per side.
Melt 2 tablespoons of butter on a large griddle over medium heat. Working in batches, add the soaked cake to the griddle and cook for 4 to 5 minutes per side, until golden brown. Continue to cook the remaining cake slices, adding more butter as needed.
To serve, cut each slice of French toast in half diagonally, dust with powdered sugar, and serve with a dollop of cream cheese icing.