Using a sharp knife, slice the avocados in half by cutting in a straight line around the pit.
Place the avocado half containing the pit in your hand and face it away from you. Gently stick the tip of the knife into the side of the pit and carefully pry it out of the avocado. For a ripe avocado, the pit will pop out with little effort. You can hold a kitchen towel in your hand and place the avocado in the towel for added protection from the edge of your knife.
Place the avocado halves on a tray. Using a pastry brush, brush oil on each of the avocado halves.
Season avocados with salt.
Place the avocados on the grill, flesh side down, and grill for 3-4 minutes, until grill marks appear.
Remove the avocados and stuff with hummus, radishes, cucumber, and a pinch of paprika.