Bring a pot of water to a boil. While you wait for the water, Heat the olive oil and add the chili flakes for 30 seconds. Add garlic, then add mushrooms. Saute until mushrooms are browned, about 5 to 8 minutes.
When water comes to a boil, place the whole eggs inside with water for 15 seconds then remove with a slotted spoon. Add 1 Tbsp of vinegar and a bit of salt. With the water at a simmer, crack the eggs (two at a time if you prefer) inside the simmering water. Cook for 2 to 4 minutes, when the whites are set but the yolk still runny.
Remove with a slotted spoon. Place on a paper towel to drain, if you wish.
When mushrooms are finished, remove. With water still clinging to the spinach leaves, quickly saute in the same pan. Squeeze the lemon onto the spinach halfway through it cooking.
Place mushrooms and spinach onto a plate. Carefully place the poached eggs over top. Season with sea salt and pepper.