Preheat the oven to 205 °C (400 °F).
Place the vegetables on a baking sheet lined with parchment paper, and drizzle with olive oil. Add the gar-lic and thyme. Season with salt and pepper and stir. Spread the vegetables evenly over the baking sheet. Roast in the oven for 25 minutes.
Meanwhile, melt the butter in a large pan over medium heat. Brown the pork chops for 1 to 2 minutes on each side. Set aside on a plate.
Remove the baking sheet from the oven and stir the vegetables. Add the pork chops to the pan of vegeta-bles. Continue cooking for 10 to 12 minutes, until the vegetables are tender.
In the meantime, cook the pancetta for 4 to 5 minutes in a small saucepan over medium heat.
Add the shallots and smoked paprika to the saucepan. Cook for 1 minute, stirring.
Pour in the beer, maple syrup and cider vinegar. Bring to a boil, then simmer for 6 to 8 minutes over me-dium heat until almost all the liquid has evaporated.
Add the demi-glace sauce and bring to a boil again. Season with salt and pepper and stir.
Serve the pork chops and vegetables with the beer sauce.
