twoSum.js

/**
 * TwoSum
 * Write a function that takes a list and outputs alist of numbers
 * belonging to the list that can be summed up to the first element of the list.
 *
 * Test Cases
 * > twoSum [17, 4, 5, 6, 10, 11, 4, -3, -5, 3, 15, 2, 7]
 * 6, 11, 10, 7, 15, 2
 *
 * > twoSum [7, 6, 4, 1, 7, -2, 3, 12]
 * 6, 1, 4, 3
 */

function twoSum(array) {
  const set = new Set(array);
  const one = array[0];
  return array.filter(two => set.has(one - two));
}

Loved your approach.

A solution using only very common pieces of the language:

const twoSum = array => {
    const target = array[0]
    let awaitingFor = {}
    let results = []

    for (const number of array) {
        if (awaitingFor[number]) results.push([awaitingFor[number], number])
        else awaitingFor[target - number] = number
    }
    
    return results
}