Bring water in a 2-quart pot to a rapid boil. Meantime, drain the Shirataki noodles. Rinse the noodles in cold water for about 10 seconds. Place the noodles in the boiling water for two minutes. Drain and place the noodles in a large and dry skillet over medium-high heat. Cook and occasionally stir the noodles until they are dry. Transfer the noodles to a bowl.

Coat the bottom of the same skillet with the olive oil and heat over same heat setting. Place the fillets in the skillet, skin down. Season with salt, pepper, and dried basil. Cook for 3 minutes or until the skin side is crispy and browned. Turn the salmon fillets over, season skin side again with a little salt, pepper, and basil. Cook for 5 minutes or until browned. The salmon is ready when it flakes easily with a fork but not dried out in the center. Transfer the crispy salmon to a large serving plate, leaving space in the center for the noodles.

Coat the reserved noodles with the creamy avocado pesto. Combine well and transfer the noodles to the center of the serving plate. Garnish with fresh parsley or lemon slices. Enjoy immediately!