In a medium bowl, whisk together eggs, half & half, water, salt, and pepper until blended. Set aside.
Heat olive oil in a 10-inch non-stick skillet over medium heat. Add portobello slices and chopped stems and cook 5-6 minutes, stirring occasionally, until browned.
Remove 3 uniform mushroom slices and set aside for garnish.
Add arugula to the pan and stir until wilted, about 1-2 minutes.
Spread ingredients into an even layer across the bottom of the pan.
Pour egg mixture over the top and cook 1-2 minutes until eggs begin to set on the bottom.
Reduce heat to just above low and cover. Cook 8-9 minutes.
Remove cover and arrange reserved portobello strips, cherry tomato halves, and feta chunks on top in a decorative pattern.
Cover and cook another 5-6 minutes until egg is cooked through and feta has just begun to melt.
Carefully transfer to a serving platter, cut into wedges, and serve warm or at room temperature.