Slice the smoked sausage into even rounds and mince the garlic. Measure the remaining ingredients so everything is ready before you begin cooking.
Heat the olive oil in a large skillet with a tight-fitting lid over medium heat. Add the smoked sausage and cook for 5–7 minutes, stirring occasionally, until the slices are browned around the edges.
Add the minced garlic and cook for 1–2 minutes, stirring constantly, until fragrant. Do not allow the garlic to burn.
In a small bowl, stir together the honey, soy sauce, black pepper, salt, and red pepper flakes. Pour the mixture into the skillet and stir until the sausage is evenly coated.
Add the jasmine rice and frozen peas and carrots to the skillet, then stir until everything is coated in the honey garlic sauce. Pour in the chicken broth and bring the mixture to a boil.
Reduce the heat to low, cover, and simmer for 18–20 minutes, or until the rice is tender, the vegetables are heated through, and the liquid has been absorbed.
Remove the skillet from the heat and leave it covered for 5 minutes. Fluff the rice gently with a fork, stir the sausage throughout, and serve warm.