Preheat oven to 350 degrees. Boil a pot of water on the stove.
Rinse asparagus, pat dry and place on cutting board. Use a chef's knife to trim off 2-3 inches from the bottom of each stalk.
Once water has come to a rolling boil, reduce the heat slightly and place the trimmed asparagus stalks in the pot. Blanch the asparagus by cooking it over medium to high heat for only 4 mintues. Do not overcook!!!
While the asparagus in cooking, fill a medium sized mixing bowl with cold ice water. After 4 minutes of cooking, pour the asparagus into a colander to drain, then immediately transfer to the cold ice water. Leave cooked asparagus in cold water for 1 minute. Then drain asparagus again in colander. Set aside.
Unwrap both loaves of bread. Discard heels; then trim crusts from remaining slices. Using a rolling pin, roll each slice of bread flat.
In a small mixing bowl, mix the softened cream cheese, grated swiss cheese, mayonnaise and egg.
To assemble, place one slice of flattened bread on workspace. Spread 1 tablespoon of cheese mixture on top. Then put one asparagus spear in the center. Roll the bread slice up tightly so that the asparagus is evenly wrapped.
Slice each roll up into 3 pieces.
Melt butter in microwaveable safe dish. Dip each piece into melted butter to lightly coat.
Arrange canapés on a prepared, rimmed baking sheet. They can be close to each other, but do not overlap them.
Bake in a 350 degree preheated oven for 15 minutes (flip halfway through) or until well browned. Allow to cool off slightly, but serve warm.
Store leftovers in an airtight container and refrigerate for up to 5 days. Reheat in a 325 degree oven for 10 minutes or until heated through.