Pre-heat the oven to 425°F.
Heat a medium size skillet over medium-high heat with two turns of the pan of EVOO, about 2 tablespoons. Once hot, add the onion and garlic and cook until soft, about 6-7 minutes. Remove the pan from heat, spoon the contents into a medium size mixing bowl and let cool. Once the onion and garlic are cool enough to handle, add the chicken to the bowl with the sundried tomatoes, basil, oregano, fennel, chili flakes, cheese, salt and freshly ground black pepper. Mix to combine.
Place a piece of phyllo on a nonstick cookie sheet and brush with the melted butter. Top with a second sheet of phyllo and brush with butter again. Divide the chicken mixture in half and form a one-inch-thick log the length of the long side of the phyllo dough. Roll the chicken log up in the phyllo tightly.
Cut the chicken-filled phyllo into 3 “cigars” and brush with more butter.
Repeat with the remaining two sheets of phyllo and the rest of the chicken mixture to make a total of two chicken and phyllo roll-ups (6 “cigars”). Bake for about 12-15 minutes, until golden brown.