Preheat oven to 350 degrees Fahrenheit. Grease a baking sheet, and set it aside.
Slice the Challah into ½-inch slices. (Feel free to slice them thicker, if desired.)
In a large mixing bowl, add the cream cheese, Monterrey Jack cheese, Cheddar cheese, salt, and black pepper, and mix until smooth.
Fold in the broccoli, coating it completely with the cream cheese mixture.
In a separate bowl, combine the butter, Italian parsley, roasted garlic, salt, and pepper.
Spread 2 teaspoons of the butter mixture on one side of each piece of bread.
Layer 2-3 tablespoons of the broccoli cheese filling on the other side. Top it with a second piece of bread, leaving the buttered side exposed to create a sandwich.
Repeat until all the bread has been used.
Arrange the sandwiches in an even layer on the prepared baking sheet, leaving a bit of space in between.
Bake for 15-18 minutes or until the cheese is melted and the bread is nice and toasted.
Store in an airtight container in the fridge for 3-4 days.
