In a large mixing bowl, whisk the eggs until fully combined and slightly frothy. Add the pumpkin puree, milk, brown sugar, cinnamon, nutmeg, cloves, ginger, vanilla extract, and salt, then whisk until smooth with no visible streaks or clumps.
Pour the custard into a shallow baking dish or pie plate wide enough to fit a full slice of bread.
Place one slice of bread into the custard and let it sit for 60 to 90 seconds. Flip and soak the second side for another 60 to 90 seconds, pressing gently so the custard reaches the center.
Lift the slice with a spatula and let any excess custard drip back into the dish for a few seconds before moving it to the griddle. Repeat with the remaining slices, working in batches if your dish is small.
Preheat a large griddle or cast iron skillet over medium heat for 2 to 3 minutes. Add 1 tablespoon of butter and swirl it across the surface until it melts and stops foaming.
Place 2 to 3 soaked slices onto the griddle, leaving space between them so they are not touching. Cook for 3 to 4 minutes on the first side, until the edges look set and the underside is deep golden brown.
Flip each slice once and cook for another 3 to 4 minutes on the second side. Add another tablespoon of butter to the griddle between batches as needed.
Transfer cooked slices to a wire rack instead of stacking them on a plate, which keeps the bottoms from turning soggy.
Plate the French toast while still warm, 2 slices per serving. Dust with powdered sugar if using, and top with warm maple syrup. Serve immediately for the best texture.