export let async function with params

Just export the variable, in this case a function.

Example with commonJS

index.js

let findOne = async function() {
    return 'Hello';
}

let deleteOne = async function(id) {
    return id;
}

module.exports = {
    findOne,
    deleteOne,
}

test.js

const { findOne, deleteOne } = require('./index.js');

async function test() {
    const x = await findOne();
    const y = await deleteOne(5);
    console.log(x, y);
}

test();

You have exported as,

module.exports = deleteOne();

By assigning as above, you are exporting the value returned from executing the function. You should export only function reference as below.

module.exports = deleteOne;

Corrected code:

Exporting deleteOne:

let deleteOne = async function (id) {
   return id+10
}
module.exports = deleteOne;

Importing deleteOne:

const deleteOne =  require('../public/javascripts/data')
deleteOne(5).then(function (result) {
   console.log(result)
})

if you want to have both functions in one file and export them you can do it like this

Export File:

let findOne = async function() {
    return "hello"
}

let deleteOne = async function (id) {
   return id+10
}

module.exports = {findOne, deleteOne}

in other Script:

const {findOne, deleteOne} =  require('../public/javascripts/data')

findOne().then(function (result) {
console.log(result)
})

deleteOne(5).then(function (result) {
  console.log(result)
})

Your export is wrong. What you have is

module.exports = findOne() - This will call the function and export the result, which is a Promise.

To export the function itself, don't call it: module.exports = findeOne

To export multiple functions in the same script, give them a name in the export (export an object that contains the functions):

module.exports = { findOne, deleteOne };

And import them with their name:

const { findOne } = require('<path>')