Broadway is Brit. British productions all but swept the Tonys, and more are to come. British productions and actors are also present if not dominating off-off Broadway etc. in New York.
This article in the Guardian details these assertions and offers some reasons why British theatre is so strong, and American theatre comparatively weak, especially on Broadway. The first answer is simple:
“It’s subsidy,” Levy says flatly. “It goes without saying that if you talk to theatremakers here, they wish there was government subsidy for the arts. It’s not impossible to develop excellent new work, but it’s much harder.”
UK not only has government subsidized theatre (although it is at least somewhat threatened by cutbacks there) but a long tradition of it, with institutions that have made creative use of it. As the article notes, shows have the freedom to experiment and to spend more time on building a production from a small to larger scale. Actors work all the time, and develop their skills.
Resulting productions, even when they go to commercial theatres, not only test the audience appeal but can be adapted to the Broadway stage with a fraction of the cost of mounting a new production there.
The last time the US had subsidized theatre was for a few years in the 1930s with the Federal Theatre Project. Several shows it developed became commercial hits, and artists it developed fed New York theatre and Hollywood film for the next thirty years.