In a medium bowl, add the tomatillo, scallions, cilantro, chopped pickled jalapeños, pickled jalapeño brine, lime juice, olive oil, and salt. Mix well. Incorporate the avocado and toss gently with a spoon to combine. Set aside.
In a small bowl, combine the mayonnaise with the prepared horseradish. Set aside.
On a cutting board, roll one slice of bacon around each sausage link. Place the tip of the hot dog over one end of the bacon slice, then roll the sausage around on the diagonal so that the bacon wraps around it and covers it entirely.
To make the hot dogs:
Heat a large skillet or griddle over medium heat. Add the bacon-wrapped hot dogs and cook, turning every couple minutes, until crisped and browned on all sides. Remove from the heat. When cool enough to handle, cut a slit lengthwise down the middle of each, without cutting completely through.
Raise heat to medium-high. Add two piles of about 1 cup shredded cheese onto the skillet and top each with a hotdog, slit-side down. Cook for 2 to 3 minutes until the cheese has completely melted and browned creating a cheese crust.
Meanwhile, open the buns but try not to separate the tops from the bottoms. Lightly toast the buns in the toaster or griddle. Spread a generous tablespoon of the horseradish mayonnaise onto each bun.
When bacon cheese hot links are ready, using a spatula, flip onto the bun, cheese side up. Top with a generous amount of the avocado relish, garnish with the pickled jalapeño slices and serve.