Preheat oven to 375 degrees. Line a large cookie sheet with parchment paper.
Cut the cream cheese and butter into slices and place in a food processor along with the mayonnaise, green onions and Parmesan cheese. Process until well mixed and the onions are finely chopped. Season to taste with Tabasco and kosher salt (see Note below on salt).
Generously spread cheese mixture on melba rounds. Leave a small border around the edges, as the cheese spreads a bit as it heats. Place rounds on prepared cookie sheet and bake until bubbly and lightly browned, around 12 to 15 minutes.
Let cool a bit, sprinkle with paprika and serve.
Note on melba rounds: You can substitute sliced whole wheat or white bread. Cut 1 1/2 to 2-inch rounds out of bread slices and lightly toast.
Note on salt: Adding enough salt is key to the flavor in this dish. If in doubt, add a pinch more than you think you need.