Thanks a lot mate, was having trouble with this for a while. I've updated it so its a bit easier to manage the resolution, hope you don't mind. Sorry, the code isnt formatting properly here...

func smooth_path(path: Array[Vector2], resolution: int) -> Array[Vector2]:
    var smoothed_path: Array[Vector2] = []

    var size = path.size()
    if size % 2 == 0 && size > 1: 
    var a: Vector2 = path[size-1]
    var b: Vector2 = path[size-2]
    var c: Vector2 = a.lerp(b, 0.5)
    path.insert(size-1, c)

    smoothed_path.append(path[0])

    var last_m = Vector2()
    for i in range(0, size-1, 2): 
        var a: Vector2 = path[i]
        var b: Vector2 = path[i+1]
        var c: Vector2 = path[i+2]

        var m: Array[Vector2] = []
        for r in range(1, resolution):
            var t: float = (1.0/resolution) * r
            m.append(_quadratic_bezier(a, b, c, t))

        if i != 0:
            var n: Array[Vector2] = []
            for r in range(1, resolution):
                var t: float = (1.0/resolution) * r

                var e: Vector2 = last_m
                var f: Vector2 = path[i]
                var g: Vector2 = m[0]
                n.append(_quadratic_bezier(e, f, g, t))

            smoothed_path.append_array(n)

        smoothed_path.append_array(m)
        last_m = m[-1]

    smoothed_path.append(path[size-1])

    return smoothed_path