Сам решил вот так
browserSync.init({
server: "./",
cors: true,
middleware: function (req, res, next) {
res.setHeader('Access-Control-Allow-Origin', '*');
next();
},
socket: {
domain: 'localhost:' + portForBrowserSync
},
scriptPath: function (path, port, options) {
return "http://" + options.getIn(['socket', 'domain']) + path;
}
});