Place pesto in a large bowl. If using portobellos, remove stems and gills. Tear mushrooms into 3”–4” pieces. Heat 1 Tbsp. oil in a medium heavy skillet over medium-high. Arrange half of mushrooms in a single layer in skillet and cook until they start to sizzle, then wrap the bottom of a second heavy skillet that is small enough to nestle into the first with foil and use it to press down on mushrooms evenly (apply pressure with your body weight to really smash the mushrooms into the hot skillet). Cook, pressing down and rotating pan as needed for even browning, until mushrooms shrink significantly and are deeply browned underneath, about 3 minutes. Remove top skillet; season mushrooms with salt. Turn mushrooms over, add 1 tsp. oil to pan, and re-cover with foil-lined skillet. Cook, pressing, until second sides of mushrooms are well-browned, about 3 minutes. Transfer mushrooms to bowl with pesto. Repeat process with remaining mushrooms and 1 Tbsp. plus 1 tsp. oil. Toss mushrooms in pesto to coat.