In a saute pan over medium-low  heat, add  2 tablespoons olive oil. When hot add the leeks and garlic and season with salt and pepper. Cook the leeks until tender about 4 to 5 minutes. Add the white wine or Vermouth and let simmer until almost all of the wine has evaporated.  Transfer the leeks to a mixing bowl with both cheeses. Mix well. Form the mixture into 8 (2-ounce) buttons or cakes. Season the flour and bread crumbs with salt and pepper. Dredge two buttons at a time in the flour. Dip them in the beaten eggs, letting the excess drip off. Then dredge in the seasoned bread crumbs. Transfer the buttons to a parchment lined baking sheet and continue the process until you have used all the goat cheese mixture. Transfer the baking sheet to the refrigerator and let stand for at least 30 minutes and up to overnight.

In a saute pan, render the bacon until crispy, about 5 minutes. Add the onions, bell pepper and mushrooms and cook until tender about 5 to 6 minutes. Add the lentils and the balsamic vinegar and cook until just warmed through. Set aside and keep warm over low heat.

In a saute pan, heat the remaining olive oil. When the oil is hot, add half of the buttons to the pan. Pan-fry the buttons  for 2 to 3 minutes on each side. Remove from the pan and drain on paper-lined plate. Repeat with the remaining goat cheese buttons.

Add the basil to the lentil mixture. Spoon the lentil mixture onto the center of each plate and place two of the feta and goat cheese buttons  in the center of the plate.