Bring chicken stock to a boil, stir in rice and reduce heat to simmer. Cover and cook 40-45 minutes until wild rice blooms and is tender. Drain and cool on a baking sheet then transfer to a mixing bowl.
In a skillet, heat EVOO over medium-high heat, a turn of the pan. Melt in butter then add mushrooms and sauté to soften, 5-6 minutes. Add leeks, thyme and dill, and season with salt and pepper. Cook 3-4 minutes more, deglaze with vermouth or wine. Add lemon juice and transfer to the mixing bowl with rice. Stir to combine.
Preheat oven to 425°F. Cover a baking sheet with parchment paper.
Gently roll out the puff pastry sheet with a sprinkle of flour. Cut 4 rectangles about 6x8 inches.