How to Make It
Fill a small saucepan halfway with water; bring to a boil over medium-high. Add almonds and pine nuts; cook, undisturbed, until nuts are tender, about 15 minutes. Drain and discard cooking liquid.
Process drained nuts, filtered water, lemon juice, garlic, and 1/2 teaspoon each of the cider vinegar and salt in a mini food processor until mostly smooth, about 90 seconds, stopping to scrape down sides of bowl as needed. Spoon almond mixture into a fine mesh strainer, and place strainer over a bowl so it rests an inch above the bottom of bowl. Refrigerate 12 hours. Remove strainer from bowl; discard liquid. Roll “goat cheese” into 12 balls (a little less than 1 tablespoon each) and flatten slightly. Place on a rimmed baking sheet. Freeze until ready to use.
Thinly slice 1 of the Granny Smith apples to equal 1 cup. Toss apple slices with 3 tablespoons of the apple juice and remaining 1/2 teaspoon apple cider vinegar in a small bowl; set aside. Using a sharp 1-inch melon baller, scoop out flesh of other apple, making 20 balls; reserve any remaining apple for another use.
Melt butter in a large skillet over high until just browned, 3 to 4 minutes. Add pear pieces and the 20 apple balls to butter, and cook, stirring occasionally, until crisp-tender and slightly browned, 4 to 5 minutes. Remove from heat, and stir in thyme, ginger, and remaining 2 tablespoons apple juice and 1/4 teaspoon salt; set aside.
Sprinkle sugar evenly over each “goat cheese” ball; heat with a kitchen blow torch until sugar caramelizes and darkens.
Drain sliced apples; reserve liquid. Divide arugula evenly among 4 plates; top each with 3 “goat cheese” balls. Arrange sliced apples and cooked pear mixture on top of arugula. Drizzle reserved liquid from sliced apples over salad.