1: Set up your grill for direct grilling and build a hot fire.

Stem the portobellos and wipe the caps clean with a damp paper towel. Brush each on both sides with extra virgin olive oil. Sprinkle each with chopped chives and oregano and season with salt and pepper.

2: In a bowl, toss the mushrooms with 2 tablespoons of olive oil as well as the chives and oregano. Season with salt and pepper.   Tip into a grilling basket or vegetable grill grate.

3: Heat the grill to high and brush or scrape the grill grate clean, then oil it. Grill the portobellos, gill sides down, then cap sides down, until sizzling and tender, 2 to 3 minutes per side.  Transfer to a heatproof platter. Lower the grill heat to medium-high.

4: Lightly brush the cheeses on both sides with olive oil. Sprinkle with dried oregano and hot red pepper flakes. Once again, brush or scrape the grill grate clean and oil it well.

5: Grill the cheese for 2 to 3 minutes per side, turning 90 degrees after the first minute or two for a handsome crosshatch of grill marks.

6: Arrange the grilled cheeses on top of the portobellos, one per mushroom. Gently warm the cognac to body temperature, or about 100 degrees.  Carefully ignite the mixture with a long-stemmed match. Pour the flaming cognac evenly over the cheeses and mushrooms.

7: Serve immediately with the grilled breadsticks.