Bring a large pot of water with the 1 teaspoon salt to a boil over medium heat. Add the beans and onion slices. Cook until the beans begin to turn bright green and are just tender, about 3 to 4 minutes. Remove from heat and drain. Rinse and drain well.
In a small saucepan, over high heat, bring the first 7 ingredients to a boil, then turn off the heat, stirring until dissolved. Remove from heat.
Distribute the grated fresh horseradish, lemon zest, garlic cloves, whole peppercorns, jalapenos slices among the jars.
Pack beans and onions in sterilized jars then cover with the vinegar mixture.
Fill to within 1 inch of the top. The beans should be covered and there should still be 1/2 inch of airspace left in the top of each jar.
Put the lids and rings on.
Put the lids on each jar and seal them by putting a ring on and screwing it down snugly (but not with all your might, just "snug").
Using the jar tongs, put the pint jars in the canner and keep them covered with at least 1 inch of water. Keep the water boiling.
Boil them for.
5 minutes for 0-1,000 ft.,.
10 minutes 1,001-6,000 ft.,.
15 minutes above 6,000 ft.
Lift the jars out of the water and let them cool without touching or bumping them in a draft-free place overnight.
Then remove the rings if you like. Once the jars are cool, you can check that they are sealed verifying that the lid has been sucked down. Just press in the center, gently, with your finger. If it pops up and down (often making a popping sound), it is not sealed. If you put the jar in the refrigerator right away, you can still use it.
Give it a weeks time for the seasonings to be absorbed into the pickled beans.
Process in a hot water bath, remove and cool in a draft free spot for 24 hours.
You can also put them in sterilized jars and refrigerate instead of doing the canning process. Let flavors meld for 1 week. Just keep under refrigeration and eat within 1 month.