Prepare the vinaigrette by combining sesame oil, vegetable oil, minced shallot, rice wine vinegar, lemon juice, and soy sauce in a blender.

Process the ingredients until smooth.

Set the vinaigrette aside.

Heat vegetable oil in a small heavy skillet over medium-high heat.

Add one-third of the sea parsley to the hot oil.

Cook, stirring occasionally, until the sea parsley is crispy, approximately 4 minutes.

Remove the crispy sea parsley with a slotted spoon and drain on paper towels.

In a large bowl, combine carrots, jicama, cucumber, and the remaining fresh sea parsley.

Toss the vegetables to combine.

Pour the vinaigrette over the salad and toss again to coat evenly.

Crush the fried sea parsley.

Sprinkle the crushed fried sea parsley and toasted sesame seeds over the salad.

Serve immediately.