Place the oven rack on the middle rung; preheat oven to 450 degrees F.
If your pizza crust is unbaked, pre-bake it for 5 minutes.
Combine the olive oil and pesto, then spread crust with the mixture.
Place eggplant and mushrooms evenly over the pesto, then sprinkle with the feta cheese.
Season the pizza with salt and freshly ground pepper, to taste.
Bake on pizza pan or on pizza stone in preheated oven for 15 to 20 minutes or the eggplant is cooked to preference, the crust edges are golden, and the feta is soft and beginning to brown (make sure to check it occasionally so that pizza doesn't burn).
Note: those folks who like it a bit spicier can garnish their servings with red pepper flakes; also it's even better if you use prepared eggplant - take a look at my posted recipe "Hopvine's Marinated Roasted Eggplant".