Prepare the pot pies dough: Place the flour, salt, and sugar in a bowl in the bowl of an electric mixer fitted with the paddle attachment. Beat in the butter at low speed until mixture is well combined yet lumpy. Add the egg and beat until just incorporated. Add the iced water and beat until obtaining an homogeneous mixture. You might need to stop the electric mixer a few times to scrape together dough from both bottom and sides of the bowl.
Place the dough onto a floured surface, form a ball, and then press into a flat disk. Wrap in plastic wrap and refrigerate for about 1 hour.
Meanwhile, prepare the pot pies filling. In a medium stainless steel saucepan, bring the chicken stock or broth to a boil over high heat. Reduce the heat to low and stir in tomato paste, whisking to dissolve.
In a different saucepan, melt the butter over low heat, add the flour, and stir well to make a roux. Add a little bit of the warm stock, whisking well until combined. Add the remaining stock and continue to whisk well constantly, over medium heat, until it thickens. Season with salt and pepper to taste and set aside.
Heat the olive oil in a medium saucepan over medium heat. Add the onion and cook, stirring occasionally, until soft and translucent. Reduce heat to low, add the garlic, and cook for about 1 minute, stirring occasionally. Add the crushed tomatoes and let cook for about 1 minute. While tomatoes are cooking over low heat, process shrimp in a food processor until obtaining a lumpy mixture (with small pieces, not minced). Add shrimp, hearts of palm (optional), corn, and olives. Stir in and let cook for about 1-2 minutes. Season with salt and pepper. Remove from the heat.
Stir in the shrimp mixture into the creamy chicken stock/broth. Add the chives or green onions, taste, and adjust the seasoning (salt and pepper) if necessary. Let filling cool before using. Meanwhile, remove the dough from the refrigerator for 15-20 minutes before rolling.
On a lightly floured surface (or a surface covered with a plastic sheet), roll the dough (using a floured rolling pin) into a very large circle about 1/16 inch thick (thin dough), working from center to edges. If easier, you can also cut the dough in half and roll into 2 large circles. Using a 6 cm (2-1/3 inch) and a 4-1/2 cm (1-3/4 inch) round cutter, cut about 48-50 discs of the larger size and a matching number of the smaller size. You might need to gather the leftover pieces of dough to obtain the full number of discs. To do this, form all the leftover dough into a ball, roll the dough again into a circle, and cut out additional discs.
Use a metal spatula to help lift the discs, and place the larger discs into the wells of 2 (24-count) mini muffin baking pans, forming a mini cup (about 48-50 discs). Using a 1/2 tablespoon, scoop filling into each dough cup. Cover each dough cup with the smaller disc, pinching the edges together gently to seal. If desired, use a fork to make a patternaround the edges. Using a paring knife, cut a tiny slit in the center so that steam can escape. Brush top with beaten egg and refrigerate mini pot pies for about 15 minutes.
Preheat the oven to 350 degrees F (about 180 degrees C). Bake mini pot pies for 13 -15 minutes, or until lightly brown.
Place muffin pans on a rack and let cool just enough to handle shrimp mini pot pies. Serve pot pies warm by themselves or accompanied by a rosé sauce.