This is a fixed construction in which:
1 A verb is used towards the end of a clause.
2 The same verb, as a bare infinitive, is used immediately after, in the set phrase And {verb} they have. (The subject can be any nominative personal pronoun: for example and {verb} he has (Number 6)).
3 Obviously the close approximation of the same two words is a rhetorical device of repetition. Or, in simpler terms, it just makes the second clause sound cool.
In your example, but is used instead of and. I guess the author wants to say something like but (contrary to expectations) build they did.
4 Note that the word that is repeated is not a simple noun. Although build, come, and rot (Numbers 1,2,3) can be nouns, they are not nouns here. Note in Numbers 4, 5, 6 that succeed, lose, and suffer are not nouns.
No. 1
... This is certainly the best work that Microsoft has done in the arena of programming languages and programming environments. Of course, they had the considerable advantage of being able to see what worked well and what didn't work so well in Java, and build upon that, but build they have.
No. 2
“Really, it's all about exposing the game,” says Dawick, “Even though lacrosse is our national summer sport, people are still not aware of our game. First and foremost, it was about bringing in the right people and getting the franchise headed in the right direction, then do everything in our power to share our message and vision. The game will sell itself, I’m sure of that. It's about getting the people out; they will come back.”
And come they have – in droves...
No. 3
This is the SE corner of the yard. I tossed the Halloween pumpkins here to rot, and rot they have...
No. 4
“Being a twin you’re always going to have some kind of competition, and we both grew up trying to beat each other,” said Jennifer. “But when you come to college you compete for a team. We became teammates. We’re not big rivals now—we’re in it together and we want each other to succeed.”
And succeed they have. Both sisters...
No. 5
Making any comment would be worse than making no comment, as that would only encourage people who have let it go to get back into the fray.
The only way to win is not to play the game.
Nope, that is the only way to lose. And lose they have.
No. 6
Archbishop Burke is not only a wise counselor on matters pertaining to Canon 915 — which requires bishops, priests, deacons and extraordinary Eucharistic ministers to protect Christ from sacrilege by denying Holy Communion to public figures who favor such sinful actions as abortion — but he is loyal to his Lord regardless of the ridicule he might suffer.And suffer he has!