A "full strength" braggot isn't going to be much faster to make than your typical mead. You can make a lower alcohol beverage (say 6% abv) that can be ready to go in a month or so.
You can make a low alcohol mead, just add less honey. It will be much thinner in body, however, and might taste watery next to a 12-14% example. You can boost mouthfeel with some carbonation or residual sugar. Residual sugar from honey is hard to do with a low alcohol product, but malt gives you opportunity to add unfermentable sugars. You could call this a braggot if you like:
Honey to SG 1.040
Crystal malt, enough to move SG to 1.050
Ale yeast, I'd suggest something like Nottingham or Windsor (available in dry form)
Ferment for about 2 weeks, bottle with ~0.75 oz (weight) of cane or corn sugar per gallon or ~0.9 oz (weight) of honey per gallon, bottle in pressure-safe bottles (like 12 fl oz beer bottles).
Let condition at room temp for 2 weeks, refrigerate and enjoy.
No hops, no bitterness, just some sweetness from the malt. You can easily modify this to add some spices, herbs, etc. If you make it much sweeter I would suggest putting something in there for bitterness or tannins to balance.
Let us know how much volume you're looking for and we can give you an estimate of honey and malt quantity.
Update: A quicky recipe
6 lbs honey (your choice)
2 lbs Crystal 40 (medium amber) or 1 lb each Crystal 40 and Crystal 80 (darker)
1/4 to 1/2 oz medium AA hops (Cascade, Goldings, Mt Hood, Willamette, etc)
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Steep grains in 1.25 gallon water at ~130-160 F for 20 mins. Remove grains (use a strainer bag for example). Boil liquid for 10 minutes, add hops, continue boiling for 20 mins. Turn off heat, cover and let cool to <150 F. This is now "wort".
Mix honey into 2 gallons of cool water. Add wort. Add cool water to get to 5 gallons.
When temperature is below 70 F, pitch yeast (rehydrate per package directions).
I added some hops in here just for the bacteriostatic properties, which helps with low alcohol stuff. You'll get a little aroma & flavor from them too, but barely any bitterness. You can still add spices and such, the hop contribution will not get in the way. You can of course add more hops, or boil longer to extract more hop bitterness. Even if you boil for 60 mins with the hops, the bitterness will be very low.