Purée squash, water and smoked paprika in a blender or food processor. Set aside.
Heat oil in a 10-inch skillet over medium-high. Add sage and garlic, and cook 30 seconds, or until the garlic is fragrant. Stir in the squash mixture and red pepper flakes, and let it come to a simmer.
Reduce heat to medium, and make 4 indentations in the sauce with the back of spoon. Crack 1 egg into each indentation. Cover, and cook 6-8 minutes, depending on how set you like your eggs. Garnish with salt, pepper, and parsley or cilantro.