Heat your oven to broil and place a rack in the upper middle position. Line a baking sheet with aluminium foil.
With the olive oil, brush the bread on both sides, and season with salt and pepper. Place the slices on a baking sheet and place into the oven for 1–2 minutes each side, until lightly toasted.
Remove the bread slices and set aside. Place ham slices on a baking sheet, and broil 2 minutes each side, until they begin to brown. Remove the ham slices and set aside.
Cover the bread slice with a slice of cheese. Place the ham so it covers about 2/3 of the bread slice.
Top the ham with apple slices. Arrange the avocado slices on the other 1/3 of the bread slice.
Repeat for remaining slices of bread.
Broil for 3–4 minutes, or until cheese starts to melt. Remove from the oven, drizzle with honey, and sprinkle a bit of salt and pepper. Serve while warm.