Merge Overlapping Intervals

You are given a list of intervals where each interval is represented as a pair of integers [start, end]. Some intervals may overlap, and your task is to merge all overlapping intervals into one and return the resulting non-overlapping intervals in sorted order.

For example, given the input:

[[1, 3], [2, 6], [8, 10], [15, 18]]

The merged intervals would be:

[[1, 6], [8, 10], [15, 18]]

Write a function that accepts a list of intervals and returns a new list where all overlapping intervals have been merged. Your solution should consider the efficiency and correctness of the merging algorithm.

Consider edge cases such as an empty list of intervals or intervals that do not overlap at all.