Place cucumber in a blender, cover and process until smooth. Place 3/4 cup of puree in a saucepan (discard remaining puree or save for another use). Add the sour cream, water, sugar and salt to pan; heat to 120°-130° (mixture will appear separated).
In a large bowl, combine 1-1/4 cups flour, yeast, chives and dill; add cucumber mixture. Beat on low speed just until moistened; beat on high for 3 minutes. Add enough remaining flour to form a stiff dough.
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.
Punch dough down; let rest 10 minutes. Shape into 12 balls; place in a greased 13-in. x 9-in. baking pan. Cover and let rise until doubled, about 45 minutes.
Bake at 375° for 30-35 minutes or until golden brown. Remove from pan and cool on a wire rack for 10 minutes. Serve warm.