For Three Kings Day we went as far east as NYC, eating food that a wise guy in the Bronx might. I boiled up dirty water dogs (although I usually use dry heat in a pan and get a nice sear, I wanted to be authentic) and served them with mustard, sauerkraut, and onion relish. Now, you might think that sounds like too many pungent/sour/funky ingredients. But it's a thing because it works. I like it better than a ketchup and mustard dog.
The only thing that really needed preparing was the relish, and although I was skeptical about my ability to make it 'right,' it turns out I quite liked my version. (It's been too long since I've had a street cart dog to honestly comment on authenticity, but it matched my sense memory well). I combined a few recipes from the web; one claiming to be authentic (by far the simplest), Bobby Flay's, and a little bit of Martha Stewart's (her innovation was to use tomato paste and red wine vinegar rather than ketchup).
New York Hot Dog Onion Relish
2 T veg or olive oil (I used olive oil)
2 medium sweet onions, cut in 1/4 inch slices
1 T honey
some cinnamon-- I sprinkled-- maybe 1/2 t?
some chili powder-- also, sprinkled-- maybe 1/2 t?
2 T tomato paste
~3-4 T red wine vinegar (I don't quite remember)
hot sauce-- again, by sight-- a dash or so?
1/2 c or so water-- probably more, see instructions
Heat oil over medium-high heat and saute the onions until soft. Stir in the the honey, cinnamon, and chili, and cook 1 minute. Add tomato paste, vinegar, hot sauce, and water; season with salt and pepper.. Bring to a boil, reduce heat, and simmer, stirring occasionally, until thick and glossy, 10-15 minutes. I don't know how much water I really added; I added more because I wanted it to cook longer and it had used up all the water. So add more and cook it down to a jam. Taste and use salt until the flavors really pop. Cool to room temperature. Serve on an all-beef dog (my strong preference) with mustard (I like spicy brown or hot) and sauerkraut.