How to use async function as parameter in TypeScript

async function useCache(
    collectionName: string, 
    key: string, 
    response: functions.Response<any>, 
    fetch: () => Promise<any>
): Promise<any> {
    const existing = await db.collection(collectionName).doc(key).get() 
    if (existing.exists) {
        response.send(existing.data())
        return
    }

    const object = await fetch()
    const json = Object.assign({}, object)
    await db.collection(collectionName).doc(key).set(json)
    response.send(object)
}

useCache(
     "books",
     key,
     response,
     async () => {
         const service = new Service()
         return await service.doSomething(key)
     }
)