Preheat oven to 350°. Toast hazelnuts on a rimmed baking sheet until fragrant and golden beneath skins, 11 to 12 minutes. Rub in a kitchen towel to remove loose skins, then chop roughly.
Whisk together oil, vinegar, mustard, honey, salt, and pepper in a large bowl. Add lettuces, onion, mint, and nuts and gently toss to coat. Tuck in figs and cheese.
6 Figs to Try
Once dominated by dried fruit, California's fig industry, centered in the Central and Coachella Valleys, now sells a number of fresh varieties as well. Each is a little different--so try them all. Fresh figs are perishable; chill, loosely wrapped, up to 3 days.
Black Mission. Purple-black skin and vermilion flesh; earthy, floral flavor.
Brown Turkey. Purple-chocolate exterior; full, fruity flavor.
Calimyrna. Pale yellow; buttery sweet, nutty flavor.
Kadota. Light green skin changes to amber as it ripens; delicate flavor.
Sierra. Another green variety; lightly aromatic with a hint of summer berries.
Tiger (aka Panache). Green stripes on the outside, red inside; berry flavors.
*Find Little Gem lettuce, a kind of miniature romaine, at farmers' markets and well-stocked grocery stores.