There are veggie bread pudding quiche like recipes - I've never made them though... worth googling.
I think bread pudding is my favorite way to use old bread - easy and really yummy - although I find many recipes are way too full of sugar for my liking. I found a recipe from weelicious.com that I like (and I'm sure you could use milk other than cow's milk):
Breakfast Bread Pudding (Makes 4-6 Servings)
3 Large Eggs
3/4 Cup Milk
3 Tbsp Honey, or to taste
1 Tsp Vanilla
1 Tsp Ground Cinnamon
Pinch Salt
2 Small Apples, peeled, cored and cut into small dice (I like Gala, Fuji or Golden Delicious)
1/3 Cup Raisins
5 Slices Whole wheat or Multigrain Bread (fresh or stale bread), cut in 1-inch cubes (about 4 cups)
1. Preheat the oven to 350°F.
2. Butter a 1 1/2-quart, 8-inch square baking dish.
3. Beat the eggs, milk, honey, vanilla, cinnamon and salt in a large bowl.
4. Stir in the apples, raisins and bread cubes. Using your hands or a rubber spatula combine the ingredients to make sure everything is evenly coated.
5. Transfer the mixture to the prepared dish pressing down lightly. Cover with foil and allow to rest for 15 minutes.
* You can prepare the breakfast bread pudding ahead at this point. Cover and refrigerate overnight.
6. Bake for 30 minutes covered. Uncover and continue to cook for an additional 20 minutes. Bake until golden and cooked through.
7. Serve.
I skip the raisins and apples for my crew and add smashed bananas. Applesauce would also work very well, I imagine. I also add more cinnamon than called for and a bit more honey. It's not overly sweet and it really is a great breakfast food. Nice and filling.
Makes me want to have more old bread around just so I can make it more often!