Brown the chopped bacon in a skillet over medium heat, stirring often. Cook until very crispy, then remove with a slotted spoon onto a paper towel to drain grease.
Slice each Brussels sprout in half vertically, then lay each half flat on the cutting board and cut into thin vertical strips. To slice the broccoli, first remove the thick stems, then cut the florets off. Additionally slice any florets so that they're uniform in size.
To make the dressing, first combine the vinegar, garlic, and Dijon mustard in a small bowl. Whisking constantly, slowly pour the olive oil into the mixture until mixture becomes opaque. Sprinkle in salt and pepper to taste.
Combine the bacon, Brussels sprouts, broccoli, pine nuts, and goat cheese in a large bowl. Pour dressing over contents and toss well to combine.