Set the oven at 200C/gas mark 6. Place a piece of kitchen foil in a large roasting tin. Wash the beetroot and trim their stems, taking care not to puncture the skin.
Add the thyme sprigs, water and 2 tbsp of the oil, then loosely scrunch the edges of the foil to make a parcel. Bake for 45 minutes until the beetroot is just showing signs of tenderness.
Peel and roughly chop the onion and garlic and mix with the remaining oil. When the beetroot has been cooking for 45 minutes, add the onion and garlic mixture to the roasting tin around the foil parcel and return to the oven.
Continue cooking for a further 40 minutes or until the beetroot is tender and the onion mixture is sweet and caramelised.
Unwrap the beetroot, let it cool briefly, then peel off the skin by rubbing with your thumb. Put it into a processor or blender with the onion-mixture vinegars, a generous seasoning of salt and the horseradish, added to taste, if you like.
Check the seasoning for vinegar. Process to a coarse purée. The ketchup will keep in a sealed jar for up to a week in the fridge.
To cook the chops, put the peppercorns and salt in a mortar. Pull the leaves from the thyme and bash with the seasonings with a pestle or heavy weight. Lightly oil the chops then rub the thyme seasoning into them.
Cook on a heated griddle until the fat is golden and translucent.