Begin by pouring the chicken broth into a large saucepan and bringing it to a rolling boil over medium-high heat. Add the broccoli florets to the simmering broth, then reduce the heat. Cover the pan and let the broccoli cook gently for about 5 to 8 minutes, or until it reaches a crisp-tender texture while retaining its vibrant color.
While the broccoli is simmering, heat the olive oil in a large skillet over medium heat. Add the julienned sweet red pepper and chopped shallot. Sauté for around 5 minutes, stirring occasionally, until the vegetables are tender yet still slightly crisp, releasing a subtle sweetness and aromatic depth.
Once the broccoli is done, drain it thoroughly and transfer it into the skillet with the sautéed red pepper and shallot. Add the slivered almonds, lemon-pepper seasoning, and salt. Toss everything together and cook for another 2 minutes, stirring continuously to combine the flavors and allow the broccoli to finish cooking to perfect tenderness.
Serve warm for a vibrant, flavorful vegetable side dish that combines texture, color, and a hint of citrusy spice.