[jyl]

Not enough info.

What is the breezeway used for now? Is that how people get from garage to house? When you enter the red door, what's there? Is that the main/only entrance to the house, or is there a main/formal front door somewhere else? Does your weather suck or is it nice? Where is south, where is the sun? Does wind currently whip through that tunnel or is it sheltered? Do you already have plenty of patio space? Do/will you need ramp (handicap) access? What problem/need are you trying to solve/address? Or are you simply looking to fill the hole with something better-looking?

My 2/10th of a cent, without actually any info, is -> if the house doesn't have a well-defined main entrance, I'd make one. If the wall between the red door and the basement access is the logical place, then the area you've dug up seems big enough for broad steps, an entry deck/porch, something to frame the entrance. Or, the breezeway could itself be the made into a main entrance, assuming the red door leads somewhere appropriate, not to a kitchen or mudroom.

My impression is that this is a nice big house with that grand tree and all that beautiful shake. It needs an entrance with some drama and grandeur.