Toast the walnuts in a medium-hot sauté pan or grill pan and set aside in a bowl until time to assemble the salad.  Let cool, then crush into large pieces with a flat-bottomed measuring cup or glass.

Heat 2 Tbsp. oil in a large skillet, preferably cast iron, over medium-high. Cook peppers in a grill pan turning peppers occasionally until skins are lightly charred and flesh is tender, 6–8 minutes. Transfer peppers to a cutting board and let cool slightly.  If using large peppers, cut in half lengthwise.

Combine ricotta and 2 Tbsp. oil in a small bowl; finely grate the zest from lemon over and mix well. Season lemon ricotta with salt. Set lemon aside.

Combine peppers, cucumbers, mint, and half of walnuts in a large bowl. Cut the preserved lemon in half and squeeze the juice into a bowl. Drizzle in 2 Tbsp. oil, season with salt and toss to coat.

Transfer pepper mixture to a platter along with any juices in the bottom of the bowl. Dollop lemon ricotta over and top with remaining walnuts. Drizzle with more oil and season with black pepper.