"recursion" in a function argument via callback

Now I get it, your problem is not really recursion itself but immutability. You can do it with a ref.

type opts = {foo: React.element}

@val
external registerSW: opts => unit => unit = "registerSW"

let updateSWRef = ref(ignore)

updateSWRef :=
  registerSW({foo: <button onClick={_ => updateSWRef.contents()} />})