If the aluminum nose is broken off from the starter, the armature shaft should have come out with the rest of it. So, there should be a hole in the center about 1/2" in diameter, possibly with the bearing and seal still stuck in it unless those both came out with the armature and body.
If the bearing is out, smear a small amount of grease into the hole with your finger to catch and hold onto the aluminum chips that you'll be making during the next step... the thick grease coating will help to keep those cutting chips from falling into the motor.
Then use a thread tap to cut some threads into the aluminum nose just a little ways deep... if the nose begins to turn while you are cutting threads, pull on the tap as you are turning it and it will come right out.
If it holds still while cutting those few threads, then thread in a long bolt with a heavy spacer or a stack of large nuts wrapped together with tape, or whatever you have on hand that may serve as a slide-hammer weight... slid over your long bolt.
Then simply yank on the slide-hammer weight that you just built and that nose piece will pop right out of there!
Clean the corrosion in the case up good with a scotchbrite pad or some wet-or-dry sandpaper (wet-dry paper doesn't shed as much as open paper does) and smear a light coating of grease inside that bore and onto the o-ring & nose of your new OEM Honda starter.
Reinstall and ride it...
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