Heat your oven to 425 degrees.
To prep your sprouts, trim off the little root end and slice them in half through the root, discarding any dirty outer leaves but keeping any other leaves that fall off (they'll get crispy in the oven!).
On a large baking sheet, toss the sprouts and leaves with 2 tbsp. avocado oil, 1 tbsp. vinegar and 1/2 tsp. salt. Turn most or all of them cut side down so they really caramelize. Roast for 10 minutes.
Meanwhile, chop the dates crosswise into halves or thirds. Trim the ends of the green beans if necessary.
Take the sprouts out of the oven, scoot them to one side of the sheet with a spatula and add the beans to the empty half of the pan. Toss the beans with 2 tbsp. avocado oil, 1 tbsp. balsamic vinegar and 1/2 tsp. salt. (Careful, the pan is hot! You could do this separately in a bowl and then add it to the pan, but I'm lazy and don't want one more thing to wash).
Sprinkle the dates around the veggies, trying to make sure they are touching the pan so they caramelize a bit in the oven. Put the sheet back in the oven for another 10-15 minutes, depending on how big your sprouts are.
Add the veggies to a serving bowl or platter and toss them with the final tablespoons of balsamic vinegar and freshly ground black pepper. Taste and season with more salt, if necessary. Serve immediately.