```ts
/**
 * Merges overlapping intervals into the smallest list of non-overlapping pairs covering the same points.
 * @param intervals - Array of [start, end] pairs to merge.
 * @returns A new array of merged intervals, sorted ascending by start.
 */
export function mergeIntervals(intervals: number[][]): number[][] {
  if (!intervals.length) return [];

  const sortedIntervals = intervals.slice().sort((a, b) => a[0] - b[0]);
  const merged: number[][] = [sortedIntervals[0]];

  for (let i = 1; i < sortedIntervals.length; i++) {
    const lastMerged = merged[merged.length - 1];
    const current = sortedIntervals[i];

    if (current[0] > lastMerged[1]) {
      merged.push(current);
    } else if (current[1] > lastMerged[1]) {
      merged[merged.length - 1] = [lastMerged[0], current[1]];
    }
  }

  return merged;
}
```