A naturally leavening dough (1) is prepared and enriched with such fatty matter (3) as margarine. The dough strip is then subjected to a series of successive processing operations of puffing (4) that create a variable number of superpositions of alternate layers of dough and fatty matter. The laminated dough obtained in this manner is then subjected to continuous leavening in a leavening chamber (5), baked in an oven (7) and eventually stuffed, for example with a fatty cheese-and-tomato-base stuffing cream. The upper layer of the product is garnished - for example - with small strips of peppers and slices of green olives, the product being portioned (divided into portions) only in a subsequent processing phase.