Fill a medium pot with water, add 1/8 tsp of salt, and place over medium-high heat. Rinse the lentils, then add to the water once it is boiling. Boil until lentils are tender, about 15-20 minutes. Strain and cover to keep warm.
Heat olive oil in a medium sauté pan. Add the onion, celery and carrot. Cook until the vegetables are soft and brown. Add the mushrooms, thyme, 1/2 tsp salt and soy sauce. Cook until mushrooms soften and slightly brown.
Turn heat off and stir spinach into mixture until just wilted. Add the vegetable mixture and red wine vinegar to the warm lentils. Cover to keep warm.
While vegetables are cooking, fill a small pot 3/4 full with water and add the white vinegar. Bring the water to a simmer, then drop the temperature to just below a simmer for poaching (160-180°F).
Crack the eggs into a small measuring cup or ramekin. Ease the egg into the water using the measuring cup to carefully lower the egg into the pot and tip it out into the water. Allow it to cook until the whites set, but the yolk is still soft, about 3-4 minutes. Don’t over crowd the pot, make in batches if needed.
Remove the egg gently with a slotted spoon and place on a plate layered with paper towel.
Divide the lentils into 5 dishes. Drop the eggs gently back into the water to reheat for 15 seconds. Remove with a slotted spoon again, drain water and top one egg per dish. Top with parsley and fresh cracked pepper and serve immediately.