It is difficult to give accurate measurements because I can't tell from the picture how high the stoop is, but, if it were me I would taper new soil from about 2 inches from the top edge out about 3 feet. I would then add a good compost up to the top edge and cover with turf. I would then roll the new turf enhansing soil contact and lightly compacting the new soil and compost to slightly less than the top edge. Fertilise and water it in. I would guess that the hardest part of the job would be to find the proper turf grass and if you can't find it just take plugs from the grass you have.