They don't build 'em like this anymore. My lousy photo does not do justice to this house, which I assume to have been the parsonage of the First Congregational Church of East Haddam, right across the street.
In the old days, the minister was given a house to use and land to farm as part of his compensation. In the real old days, he was paid via town taxes too: The Congregational Church was the established church of CT. Not that that meant all that much: Congo churches did, and still, vote on everything - including their doctrine and their choice of pastor - within their own congregation. Zero hierarchy, for better or worse. Every person was/is considered to have his own hotline to God.
The wife typically ran the farming business: it paid the bills and kept her out of the pool halls.
Update: I think our reader is right - the addition is the part on the left. The congregation must have felt prosperous at the time.