Preheat oven to 450 F.  Put pecans on the baking sheet you’ll be using to roast the brussels sprouts, and when the oven is hot put the baking sheet in and roast 3-4 minutes or just until the pecans barely start to look browned.  Remove from oven and put the pecans on a cutting board to cool.

Trim the stem ends of brussels sprouts and cut them in half, or in quarters if they’re large.  Most brussels sprouts don’t need to be washed but if they do, use a salad spinner and spin them very dry or they won’t roast properly. 

Whisk together the apple cider vinegar, 1 tsp lemon juice, and approved oil.  Put brussels sprouts into a bowl and toss with the apple cider vinegar mixture. Grease the baking sheet with approved oil and spread the brussels sprouts out and turn each one cut side down. Roast brussels sprouts 15 minutes.

While the brussels sprouts roast, coarsely chop the pecans.  Peel the avocados and cut them into small pieces.  Toss avocado with the 2 tsp lemon juice, and season with 1/2 tsp salt and some fresh-ground black pepper.

After 15 minutes, remove baking sheet from the oven and quickly use a turner to turn the brussels sprouts over (they don’t all have to be turned over; just turn as many as you can do quickly.)  Put the baking sheet back in the oven and roast the brussels sprouts about 10 minutes more (or until they’re nicely browned, as brown as you can get them before they would start to burn.)  

Gently toss the hot brussels sprouts with the avocado.  Season to taste with a little more salt and fresh-ground black pepper.  Arrange on a serving dish, sprinkle pecans over, and serve immediately.