Preheat the oven to 230°C (210 fan). Slice the top off the garlic bulb, then wrap it in foil. Put the wrapped bulb in a large roasting tin (23 cm x 35 cm minimum) and leave to heat up in the oven.
Pop the potatoes, onions and sliced peppers in a large freezer bag. Add 3 tbsp of the olive oil, plus the thyme, paprika and a big pinch of salt and pepper, then seal the bag and shake well to coat. Tip the contents of the bag into the preheated roasting tin, pushing the foil-wrapped garlic into the corner. Bake for 20 minutes.
Put the tomatoes and padron peppers in the same seasoning bag and shake to coat. Give the contents of the roasting tin a stir, then pour over the wine and scatter the oiled tomatoes and peppers over the top. Return to the oven for 10 minutes.
Meanwhile, heat the remaining 1 tbsp oil in a frying pan and colour the Cauldron Lincolnshire Sausages all over.
Remove the traybake from the oven and set the garlic parcel aside. Reduce the temperature to 200°C (180 fan). Stir the vegetables, then snuggle the Cauldron Lincolnshire Sausages down into the mix and return to the oven for 10 more minutes.
Squeeze the roasted garlic out of its skin into a jar and add the mayonnaise and lemon juice. Blend until smooth with a handheld stick blender, adding a teaspoon or two of water if needed to make a drizzling consistency.
Remove the traybake from the oven, drizzle with aioli and scatter with fresh parsley.