To make the duck fat croutons place water, milk and butter in a saucepan and bring to a boil over medium high heat. Slowly whisk in grits and continue to whisk until mixture reaches a boil. Reduce heat to simmer. Add in salt and goat cheese. Continue to cook grits on low, stirring often until grits have softened, about 15 minutes. Remove from heat and allow to cool for 10 minutes, stirring occasionally.
Quickly whisk the eggs into grit mixture until incorporated, moving quickly in order to temper. Spray 7 by 12 inch sheet pan with nonstick cooking spray and pour mixture into sheet pan, smoothing with a spatula. Refrigerate for 2 hours.
Remove pan from refrigerator and cut grits into small squares. Transfer the squares to a plate. In a nonstick skillet, melt duck fat (enough to cover the bottom of the skillet). Once oil has reached about 325˚F, cook croutons a few at a time. Brown grit cakes for about 1 to 2 minutes per side then transfer to a paper towel lined plate.
To make the crispy poached eggs fill a nonstick skillet, half full with water. Add salt and vinegar and bring water to a simmer over medium heat. Carefully drop 3 cracked eggs into the center of the skillet. Allow to cook for about 3 to 4 minutes or until whites of egg have set. Remove the eggs with a slotted spoon. Gently place each poached egg in a bowl filled with ice water for 2 minutes, Remove each egg and pat dry. Set on a paper towel lined tray to dry. Repeat with remaining eggs.
In a medium bowl, lightly beat the 4 remaining eggs. In a shallow bowl, combine bread crumbs, flour, herbs and spices. Set aside.
In a cast iron or heavy skillet add 1 inch of vegetable oil. Heat oil over medium heat to 350˚F. Using a slotted spoon, place poached eggs one at a time into beaten egg mixture. Remove and carefully place in bread crumb mixture, using your fingers to thoroughly crust egg. Continue to use slotted spoon, place breaded egg into oil and allow to fry for about 30 seconds on each side. Remove egg from oil and place on paper towel lined plate to drain. Repeat with remaining eggs.
To make the tomato relish, add all ingredients to a medium bowl and toss to combine. Allow flavors to meld together for about 10 minutes or more before serving.
To make the dressing combine garlic, anchovy paste, lemon juice, dijon, mayo, tabasco, Worcestershire, olive oil, black pepper, salt and Parmesan cheese in a food processor. Process until smooth, then toss the greens with ⅓ of the dressing. Reserve extra for drizzling on top or for another use.
To serve, divide tossed greens between six plates and top each with a fried egg, tomato relish and some duck fat grit croutons. Serve immediately.