1 1/4 cups plus 2 teaspoon grapeseed oil, divided
1 cup packed fresh cilantro leaves and stems
2/3 cup packed fresh flat-leaf parsley leaves and stems
1 large pasteurized egg yolk
5 1/2 teaspoons fresh lime juice, divided
1/4 teaspoon kosher salt, plus more to taste
2 large firm-ripe avocados, unpeeled, halved lengthwise, pits removed
2 cups delicate greens (such as fava leaves, ice plant, pea tendrils, or chrysanthemum greens)
Sel gris, to taste

Process 1 cup grapeseed oil, cilantro, and parsley in a high-powered blender until hot, about 2 minutes. Line a fine wire-mesh strainer with a double layer of damp cheesecloth. Pour oil mixture through prepared strainer into a bowl; discard solids. Set cilantro oil aside.

Whisk together egg yolk and 1 1/2 teaspoons lime juice in a medium bowl. Whisking constantly, very slowly drizzle in 1/4 cup grapeseed oil until completely incorporated and mixture is creamy and slightly thickened. Whisking constantly, slowly drizzle in 1/4 cup cilantro oil until completely incorporated and mixture is thick and creamy. Whisk in kosher salt.

Heat a large cast-iron skillet over medium-high. Make 1/4-inch-deep cuts in a crosshatch pattern on cut sides of avocado halves; brush evenly with remaining 2 teaspoons grapeseed oil. Place in skillet, cut sides down, and sear until charred, about 4 minutes. Remove from skillet, and let cool completely, about 15 minutes. Cut each avocado half lengthwise into 2 pieces. Carefully peel and discard skin.

Arrange 1/2 cup greens on each of 4 serving plates. Top each with 2 avocado quarters. Drizzle evenly with remaining 4 teaspoons lime juice, and sprinkle with sel gris. Arrange small dollops (about 11/2 tablespoons per plate) of cilantro mayo on greens around avocado. Drizzle each plate with 2 teaspoons cilantro oil. Serve immediately.

CHRISTOPHER KOSTOW and DAVID GUILLOTY