Given the immunity of mythos beasties tend to have against impaling weapons, and the way armor and automatic weapons function in COC rules, I say...
...for your military investigators who can get one on their humvee.
Or if they are on foot...
This assumes a modern setting of course.
Or, if they are really well connected, some kind of laser designator (SOFLAM) with an A-10 circling overhead.
Now that I think of it, a fully-automatic shotgun like the AA12 should be able to bring down a shoggoth, assuming short range (minimum damage 4), and a 20-round drum (20 x 4 = 80 hp). You could fire all the rounds in about 4 seconds.
Or better yet, two of them at medium range (damage 2 x 40 = 80).
The AA12 has practically no recoil, so you wouldn't have the same problems of barrel-climb associated with machine pistols and submachineguns.
As iron sharpens iron, so one man sharpens another. Proverbs 27:17 (NIV)