In a large bowl, combine flour and salt. Cut in butter and shortening until mixture resembles coarse crumbs. Gradually add water, tossing with a fork until dough forms a ball; flatten into a circle. Chill for at least 3 hours or overnight.
For filling, place the chicken, water, bay leaf and garlic in a Dutch oven. Bring to a boil. Reduce heat; cover and cook for 30-40 minutes or until chicken is tender. Remove and debone chicken; set aside. Skim fat. Add the beans, carrots, potatoes and basil to the broth. Cover and simmer for 12-15 minutes or until vegetables are tender. Stir in the mushrooms, peas and tomatoes; cover and simmer for 3-5 minutes. Drain vegetables and reserve broth; set side
In another large kettle, melt butter. Whisk in flour until smooth. Add 1-1/2 cups of reserved stock. Bring to a boil. Cook and stir for 2 minutes or until thickened. In a small bowl, whisk together egg yolks and cream. Whisk into the sauce; remove from heat. Season with salt and pepper. Gently stir in reserved chicken and vegetables.
To assemble flowerpots, brush outsides of pots with oil. Line each with a 15x12-in. piece of aluminum foil; pressing the foil gently down into the pot and being careful not to tear it. Fill each pot with about 1-1/2 cups of filling, leaving about 1/2-in. headspace; set aside.
Roll pastry to 1/8-in. thickness; cut six 6-in. circles. Place one circle on each flowerpot, turn down the edges and flute. Cut three vents in the center of each pastry. In a small bowl, lightly beat glaze ingredients; brush over each crust. Place flowerpots on a baking sheets. Bake at 425° for 30-35 minutes or until the crust is golden brown and the filling is bubbly. Just before serving, garnish each with a seed packet on a stick.
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