Preheat oven to 400 degrees F.
In a large bowl, toss tomato, feta, oregano, hearts of palm, and portobello until well combined.
Lay 1 sheet of phyllo dough on a clean work surface and brush lightly with tomato paste. Top with another sheet of the phyllo dough. Take 1/4 of the mushroom mixture and place it on the phyllo dough, about 1-inch from 1 end, leaving a border at the bottom and top. Fold the bottom of the sheet to cover the filling, then fold the top of the sheet so that it covers the filling. Now roll the unfolded end over the filling so that a packet is formed around the filling and there are not open sides. Set on a wire rack placed on top of a cookie sheet. Repeat process 3 more times. After you have finished the 4 packets, lightly spray once with the canola oil cooking spray. Bake for 15 minutes or until golden brown. Serve warm.