Oil as needed for frying (blend of 75% pure olive oil, 25% canola oil)
Sea salt as needed
3 cups water
2 sheets (2.5 grams) unflavored gelatin
1/2 teaspoon white unflavored agar-agar powder
Acetate sheets (or food-safe plastic sheets) as needed
Slice potatoes very thin (about 1/16 inch) with mandoline. Place in bowl of salted water, soak in refrigerator about 1 hour. Drain and dry well by spinning in salad spinner or shaking in towel.
Heat several inches of oil in deep fryer (or heavy-bottomed stockpot) to 375°F; fry potato slices in small batches until light golden brown, 1 to 1 1/2 minutes, turning once oil during cooking. Drain on paper towels. Lightly salt to taste. Cool.
Crumble 8 ounces of potato chips into 3 cups water; cover tightly with plastic wrap. Reserve covered at least 48 hours in refrigerator. Reserve remaining potatoes for another use.
Cut 32 oval potato-chip shapes, 2 1/2 to 3 inches long, from acetate sheets.
Strain potato liquid though several layers of cheesecloth into small container. Discard cheesecloth and potato solids. Return liquid to refrigerator for 1 hour. With paper towel, blot excess grease.
Bloom gelatin sheets in ice water until soft, about 2 minutes.
Dissolve agar-agar in 1/2 cup of chilled potato water, reserving remainder. In small saucepan over high heat, bring to a boil, constantly stirring. As soon as liquid boils, remove from heat.
Remove softened gelatin sheets from water, squeezing out excess water. Add sheets to agar-agar/potato mixture to melt, stirring gently until smooth. Add about 1 teaspoon sea salt.
Refrigerate until liquid begins to gel but has not hardened completely, 7 to 10 minutes.
With immersion blender on low setting, carefully and slowly beat potato-chip mixture to a homogenized honey-like consistency; take care not to incorporate air or frozen chips will be too fragile. (Push blender to bottom of mixture and hold it still, blending for just a few seconds.)
With rubber spatula, spread thin layer of chip mixture (about 1/8-inch thick) over acetate cut-outs, using about 1 to 1 1/4 teaspoons of mixture per chip. Freeze for minimum of 2 hours. (May be stored for several weeks.)
Just before service, lay frozen chip on flat surface; carefully peel off acetate.
Per portion: Serve 1 chip as amuse bouche on frozen plate or standing up in ice. (Line small plate with napkin; place partial sheet of ice cubes on napkin; stand chip upright between grooves of ice cubes.)