Preheat your oven broiler to high.
Place the bell pepper quarters skin-side up on a baking sheet and broil until the skins are charred and blistered.
Move the peppers to a bowl, cover with a plate to trap the steam, and let them sit for 10 minutes.
Once cool enough to handle, peel the blackened skins off and slice the flesh into strips.
In a small bowl, whisk together the mayonnaise, mint jelly, Dijon mustard, and lemon juice until smooth.
Brush the lamb steaks and onion rounds with olive oil, then season both sides with salt and pepper.
Heat a grill pan or outdoor grill to medium-high.
Cook the lamb for 3 to 4 minutes per side, or until it reaches your preferred doneness.
Grill the onion rounds alongside the lamb until they are tender and have nice char marks.
Remove the lamb to a plate, cover loosely with foil, and let it rest for 5 minutes.
Slice the rested lamb into thin strips.
Toast the sourdough bread slices until golden.
Spread the minted mayonnaise over one side of each slice.
Layer the lamb, charred peppers, grilled onions, and arugula onto four of the bread slices, then top with the remaining bread.