Bring the lentils and water to a boil. Reduce heat to low, cover, and simmer for 25-30 minutes, until tender but not mushy. Drain excess water.
In a food processor, pulse together the parsley, pistachios, and garlic until finely chopped. Add 1 1/2 cups of the lentils, and pulse again until mostly smooth - it will be like a paste.
Mix together the pulsed ingredients and remaining lentils. Stir in the salt and Worcestershire sauce. Taste and adjust to your liking, then add the egg, and stir in the breadcrumbs ½ cup at a time.
Refrigerate for 30 minutes.
Preheat oven to 400 degrees.
Roll 1/6 of the mixture into a smooth ball. Flatten into a burger patty shape. Place on a parchment-lined baking sheet. Repeat with remaining mixture.
Bake for 20 minutes, 10 minutes on each side until golden and firm.
Top with feta cheese and sun-dried tomatoes.