Kosher salt and freshly ground black pepper(to taste)
Cook the bacon in a large skillet over medium-high heat until crispy, about 4 minutes per side. Drain on paper towels.
Discard the fat in the skillet. Add 1 tablespoon of the olive oil to the skillet and heat over medium-high heat. Add the onion and brussels sprouts and cook, stirring only occasionally, until the onion is tender and turning golden and the brussels sprouts begin to brown in spots, about 8 minutes.
Add the broth and cover the pan. Let the liquid come to a simmer, then reduce the heat to medium. Steam the brussels sprouts until you can easily slide a sharp knife into them and the broth is almost evaporated, 7 to 10 minutes more.
To make the vinaigrette, whisk together the remaining 3 tablespoons olive oil, the vinegar, and mustard in a small bowl and season with salt and pepper.
Pour the vinaigrette over the cooked brussels sprouts in the pan and toss to coat with the vinaigrette. Crumble the bacon, add it to the vegetables, and toss one more time before transferring to a serving dish. Serve hot or warm.
What the Kids Can Do
Trim and halve the Brussels sprouts with an age-appropriate knife, crumble the bacon, whisk together the vinaigrette, and dress the Brussels sprouts.