Preheat the oven to 425 degrees Fahrenheit.
Make the marinade by combining the paprika, garlic, salt, olive oil, and vinegar in a small bowl.
Peel the carrots and chop them into one inch thick diagonal slices.
Wash and optionally peel the potatoes and cut each potato into 6 wedges.
Toss the chicken thighs, potatoes, and carrots with the marinade. If you want to do this step in advance, you can use a large ziplock bag or a bowl, and keep the marinated chicken and veggies in the fridge for several hours. If you are going to cook right away, you can toss everything directly on the sheet pan.
Spread the mixture out in a single layer on a large sheet pan, ensuring that the chicken skin is facing up to optimize for crispiness.
Roast the chicken and veggies at 425 degrees for 40 minutes. At this point, the chicken skin should be fairly crispy already, and the veggies will be cooked all the way through.
Remove the sheet pan from the oven, and brush the chicken thighs with the honey mustard glaze on both sides. Return the sheet pan to the oven, ensuring that the chicken thighs are skin side up. Bake for another 20-25 minutes until the chicken skin is very crispy and everything is very well cooked.
Optional: Use an instant read digital thermometer to check that the chicken is cooked through. It needs to be at least 165 degrees, but it will likely be much higher (185-200) because of the long cooking time.
Transfer to a serving dish (or serve directly on the sheet pan for an informal vibe), allow to rest for a few minutes, and enjoy.