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In a large mixing bowl, dissolve yeast in warm water. Add the eggs, shortening, pumpkin, milk, sugars, pudding mixes, salt and 6 cups flour. Beat until smooth. Stir in enough remaining flour to form a soft dough (dough will be sticky).
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Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
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Punch dough down; divide in half. Roll each portion into a 12-in. x 8-in. rectangle; brush with butter. Combine brown sugar and cinnamon; sprinkle over dough to within ½ in. of edges.
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Roll up jelly-roll style, starting with a long side; pinch seams to seal. Cut each into 12 slices. Place cut side down in two greased 13-in. x 9-in. baking pans. Cover and let rise until doubled, about 30 minutes.
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Bake at 350° for 22-28 minutes or until golden brown. In a small mixing bowl, combine the water, butter and cinnamon. Add confectioners’ sugar and vanilla; beat until smooth. Spread over buns. Serve warm.