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Preparation Place rack in upper third of oven; preheat to 425°F. If you see or feel dirt in leeks, rinse well, separating layers, then pat dry; otherwise, leave rounds intact.
Heat 1 Tbsp. oil in a 10" cast-iron or other deep, heavy, ovenproof skillet over medium-high. Cook sausage, stirring occasionally, until browned, 5–7 minutes. Add garlic and cook until golden brown, about 2 minutes more. Using a slotted spoon, transfer sausage and garlic to a plate, reserving about 2 Tbsp. oil in pan.
Return pan to low heat and add flour, 1 Tbsp. at a time, stirring to combine. Cook, stirring constantly, until mixture starts to smell toasty and is the color of peanut butter, about 5 minutes.
Stir in stock 1/4-cupful at a time. Bring to a boil, then reduce heat to medium-low. Add carrots, potatoes, and leek and simmer until carrots and potatoes are just softened and liquid is reduced by half, 10–12 minutes. Add reserved sausage and garlic, peas, dill, 2 Tbsp. lemon juice, 3/4 tsp. salt, and 1/2 tsp. pepper and stir to combine.
Remove from heat. Place pastry over skillet, tucking corners gently into sides; it won't completely cover pan. Whisk egg with 1 Tbsp. water (if not using, substitute 1 Tbsp. oil) in a small bowl and brush top of pastry. Cut four 1" slits in pastry to vent.
Bake pot pie until pastry is beginning to brown and underside is cooked, 23–25 minutes. Let cool 10 minutes before serving.
Meanwhile, whisk remaining 4 Tbsp. oil, 2 Tbsp. lemon juice, 1/2 tsp. salt, and 1/4 tsp. pepper in a large bowl. Add spinach, arugula, radishes, cilantro, parsley, and almonds and toss to combine.
Divide pot pie among plates and serve salad alongside.
Cooks' NoteAny brand frozen puff pastry works; the weight may vary, but either way, you'll have enough to work with.