In a bowl mash the avocado with a fork. Mix in the lemon juice, tahini, extra virgin olive oil and garlic until combined. Season to taste with salt and pepper, cover and set to one side.
Place a grill pan over a high heat. Halve the cucumber lengthways and cut into bite-size chunks. Toss with the olive oil and season with salt and pepper. Once the grill pan is very hot, add the cucumber and fry for 2–3 minutes on each side until golden and charred.
Toast the bread or plate up your rice cakes, drizzle with a little extra virgin olive oil, top with the avocado and cucumber and scatter over the parsley. Serve immediately.