In a large bowl, combine milk with yeast, sugar, and salt. Let stand 5 minutes, then add egg and beat well to combine.
Add squash and shortening; mash with a fork until shortening is in small pieces. Add 1 1/2 cups flour and mix well with a wooden spoon. Gradually mix in more flour by the cupful until dough collects around spoon and pulls away from sides of bowl (you may not need all the flour).
Transfer to a lightly floured surface and knead 2 minutes. Put dough in a greased bowl; cover with a towel. Let rise in a warm place until doubled in size, 1 to 1 1/2 hours.
Preheat oven to 400° and butter a large baking sheet. Punch dough down, turn out onto a lightly floured work surface, and knead until dough is smooth and supple, about 7 minutes. Cut dough into 4 balls; cut each ball into 6 pieces.
Roll each piece into a round and arrange rounds on baking sheet so they barely touch. Brush with melted butter and sprinkle with poppy seeds; cover with plastic wrap and let rise 30 minutes.
Bake until golden brown, about 20 minutes. Let cool, then pull apart to serve.
Note: Nutritional analysis is per roll.