Beat softened cream cheese, powdered sugar, and almond extract in a large bowl until smooth and fluffy. Start with 1/2 cup powdered sugar and adjust to taste.

In a wide shallow bowl or 9x13 baking dish, whisk together the eggs, milk, vanilla extract, almond extract, and cinnamon until fully combined.

Lay out Texas toast slices in pairs. Spread cream cheese filling on one side of each pair. Layer thin peach slices over the filling and press the second slice on top to form sandwiches. Set aside on a tray.

In a small saucepan over medium heat, melt butter. Add sliced peaches and brown sugar. Stir gently and simmer for 8 to 10 minutes until peaches are soft and the sauce is thick and glossy. Reduce to low and keep warm.

Heat a large skillet or griddle over medium heat and add butter to coat. Dip each stuffed sandwich in the egg batter for a few seconds per side to coat. Immediately place in the hot pan and cook 3 to 4 minutes per side until deep golden brown.

Transfer to plates. Dust with powdered sugar, spoon peach compote over the top, and serve immediately.