Yes, these are New York Style bagels, because there are no other bagels. Anything else is just small toroidal loaves of bread, with which one might as well not really have bothered. This is similar to the way that one can get some rather tasty Chicago-style cheese-and-tomato-sauce-bread, but not actual pizza.
(I’ve been reading Nancy Mitford, and there may be the odd little Britishism sneaking into my diction here and there.)
This recipe for six; it can be straightfowardly doubled for a dozen, or two-thirds’d for four.
Six Bagels
1 1/4 cups warm water
1 Tbs or ~2 packet active dry yeast
3 Tbs sugar
2 Tbs veg oil
1 tsp salt
5 C or so (bread) flour
One pot of water
2 Tbs or so of barley malt syrup (or honey)
Dissolve yeast and sugar in warm water, gradually add flour, oil, and eventually salt, until it begins to be dough. Do not add the entire 5 cups of flour; stop when the dough is kneadable but not dry.
Knead the dough well, and then put into a covered bowl to rise for an hour in a warm draftless place, or a couple of hours in a cool draftless place, or (ideally) overnight in the refrigerator.
Punch down and form into six tori. I find the best way to do this is to make six spheres, and then flatten each one, poke a hole in the center, and spin it around a bit on your fingers to make the hole gently larger.
(There is also the “make a snake and then convince the head and tail to stick together” method, but I find (perhaps especially when the air is dry) that this results in croissant-shaped bagels distressingly often.)
Let these rest while you preheat the oven to 450 degrees (F), boil the pot of water, and dissolve the barley malt syrup in it.
Once the water is boiling, lower the bagels in (likely three or so at a time, depending on the sizes of your pot and your tori), and boil for about one minute per side, turning them over halfway through (obviously).
Put the boiled bagels onto a sheet of baking paper on a cookie sheet.
Once the bagels are boiled and the oven is hot enough, put the cookie sheet (the one that the bagels are on) into the oven (most likely on the middle rack) for something like 15-20 minutes, or until just before the bottoms get too dark. Let cool on a wire cooling rack (or, you know, whatever).
The boiling is the key part of the recipe, and what makes them bagels rather than just weird small bread loaves. The barley malt syrup is supposedly extremely key, but I admit I’ve done it with honey instead and I won’t swear that I could tell the difference. I’ve also entirely forgotten to put anything into the water, and they were still, I would say, actual bagels.
If you compare this recipe with yesterday’s Basic Bread, you may suspect that some of the quantities don’t entirely make sense, and you may be right. The amount of flour is especially approximate; purists will know that it’s really the weight of the flour and not the volume that matters, and I don’t know the weights that I use, I just sort of put in more flour until it seems about right.
All Purpose Flour may be used instead of Bread Flour, and it will be easier to knead and somewhat less chewy and bagel-like (but still bagels) as a result.
You may use barley malt syrup instead of some or all of the sugar. This is said by some to be even more authentic, but note that (1) the substitution ratio is for you to figure out, (2) barley malt syrup is considerably harder to obtain than sugar and if you do this you will run out faster, and (3) if you keep your syrup in the refrigerator after opening (which one in instructed to do), you will want to warm it up and dissolve it in the water, rather than attempting to incorporate a basically solid lump of cold syrup into your flour mixture.
And that’s it! It’s really not a big mystery, which leads one to wonder why the things sold as “bagels” in (for instance) Florida, appear to be small toroidal loaves of bread instead. Possibly it’s something about the water, in which case I can only advise using water from within say 80 miles of New York City in the above recipe, just to be on the safe side.
ceoln 
Hm?