Is there a way to update the TLS certificates in a net/http server without any downtime?

I have a simple https server serving a simple page like so (no error handling for brevity):

package main

import (
    "crypto/tls"
    "fmt"
    "net/http"
)

func main() {
    mux := http.NewServeMux()

    mux.HandleFunc("/", func(w http.ResponseWriter, req *http.Request) {
        fmt.Fprintf(w, "hello!")
    })

    xcert, _ := tls.LoadX509KeyPair("cert1.crt", "key1.pem")

    tlsConf := &tls.Config{
        Certificates: []tls.Certificate{xcert},
    }

    srv := &http.Server{
        Addr:      ":https",
        Handler:   mux,
        TLSConfig: tlsConf,
    }

    srv.ListenAndServeTLS("", "")
}

I want to use a Let's Encrypt TLS certificate to serve the content over https. I would like to be able to do certificate renewals and update the certificate in the server without any downtime.

I tried ruing a goroutine to update the tlsConf:

go func(c *tls.Config) {
        xcert, _ := tls.LoadX509KeyPair("cert2.crt", "key2.pem")

        select {
        case <-time.After(3 * time.Minute):
            c.Certificates = []tls.Certificate{xcert}
            c.BuildNameToCertificate()
            fmt.Println("cert switched!")
        }

    }(tlsConf)

However, that doesn't work because the server does not "read in" the changed config. Is there anyway to ask the server to reload the TLSConfig?