Step 1

Spoon some ice cream into 1 cone, packing gently to fill. Dip large (1/4 cup) round ice cream scoop into bowl of hot water. Scoop large mounded ball of ice cream onto cone, pressing gently. Stand cone in small glass; place in freezer. Repeat with remaining cones and ice cream, placing each cone in individual glass. Freeze 2 to 8 hours.

Step 2

Place bittersweet chocolate and oil in small glass bowl. Microwave on medium-high until chocolate is melted, stopping occasionally to stir, about 1 1/2 minutes. Let stand just until cool, about 10 minutes. Place white chocolate in another small glass bowl; melt in microwave on medium-high, stopping occasionally to stir, about 1 minute.

Step 3

Place nuts on plate. Working quickly and tilting bowl of bittersweet chocolate to form deep pool, dip ice cream end of cone into chocolate, turning to coat. Gently shake cone, allowing excess chocolate to drip back into bowl. Immediately roll bottom half of chocolate-dipped scoop in nuts. Dip fork into white chocolate; drizzle lines over top of cone. Place cone in glass; return to freezer. Repeat with remaining cones. Freeze 1 hour. DO AHEAD: Can be made 1 day ahead. Wrap cones in foil; keep frozen.