Pour the condensed tomato soup into a gallon-sized sealable plastic bag. Squeeze the air out, seal, and place on a small baking sheet or other small, flat surface. Make sure the soup is evenly distributed in the bag and transfer to the freezer. Freeze until solid, about 30-45 minutes.
After about 25 minutes (or when the tomato soup just starts to feel like it is firming up), start to roll the bread out. Using a rolling pin (or even the empty soup can), gently flatten the sandwich bread slices, crust and all. Brush the edges of the bread with beaten egg to help seal. Place a slice of cheese in the center of each slice of bread. Set aside.
Take the frozen tomato soup out and cut open the plastic bag to remove. Use a sharp knife to cut the frozen tomato soup into sticks that will fit on top of the cheese– roughly the size of a julienne cut. See the recipe video in the blog post for a visual example.
Working quickly, place a tomato soup stick on top of the cheese, at the edge closest to you. Roll the bread tightly over, and continue to roll so that the tomato soup is in the center. Gently pinch the sides to seal. Repeat until all of the Grilled Cheese Tomato Soup Sticks have been formed, popping the tomato soup back in the freezer in between if it starts to soften too much to handle.
Melt 2 tablespoons of butter in a large skillet over medium heat. Place the Grilled Cheese Tomato Soup Sticks in the skillet, seam-side down, in batches of 3-4. Allow them to lightly brown on the bottom and then turn occasionally until browned all over as desired. Add additional butter as needed to the skillet and repeat until all of the sticks have been fried.
Allow the sticks to cool for 5 minutes and sprinkle with chopped chives. Serve warm.