In a medium bowl, beat together 3 eggs and 3/4 cup milk until combined.
Add 1/4 cup all-purpose flour, 1 tablespoon granulated sugar, 1 teaspoon vanilla extract, and 1/4 teaspoon salt; beat until smooth and well combined.
Strain the custard mixture through a wire mesh strainer into a second bowl to remove any lumps; discard solids left in the strainer.
Preheat a skillet or griddle to about 350°F. Brush the cooking surface with 2 tablespoons melted butter.
Working one slice at a time, place a slice of the 8 slices Texas Toast into the custard and soak briefly, about 10–20 seconds per side, flipping once so both sides are evenly coated but the bread does not fall apart.
Transfer the coated bread to the hot skillet and cook 1–2 minutes per side, until golden brown. Repeat with the remaining slices.
If desired, cut the French toast diagonally and arrange on plates.
Sprinkle 2 tablespoons powdered sugar over the French toast and serve with maple syrup.