For the Cajun seasoning: Add the thyme, paprika, garlic powder, onion powder, cayenne, celery salt and some pepper to a small bowl and stir to combine. Reserve for the tomatoes and hollandaise.
For the green tomatoes: Preheat the oven to 200 degrees F.
Slice the tops and bottoms off of the tomatoes and discard. Slice the tomatoes into eight 1/2-inch-thick slices total.
In a medium bowl, combine the flour, some salt and pepper and 2 teaspoons of the Cajun seasoning. Add the tomato slices and toss to coat.
Whisk together the milk and eggs in a medium bowl. Combine the cornmeal and breadcrumbs in another medium bowl.
Working with one slice of tomato at a time, shake off the excess flour mixture, then dip in the egg mixture to coat. Let the excess egg drip off, then add to the cornmeal mixture and turn to coat. Place on a platter and repeat with the remaining tomatoes.
Add about 1/4 inch of oil to a cast-iron skillet and heat over medium-high heat until it shimmers.
Add half of the tomatoes and fry, turning once, until golden brown on both sides, 1 1/2 to 2 minutes per side. Transfer to a paper towel-lined baking pan and fry the remaining tomatoes. Sprinkle with salt to taste if desired. Transfer the baking pan with the tomatoes to the oven to keep warm while you prepare the rest of the dish.
For the hollandaise: Fill a blender with hot water. Melt the butter in a small saucepan over medium heat and let the solids sink to the bottom. Pour the water out of the blender and dry it. Combine the lemon juice, egg yolks and 1 tablespoon of the Cajun seasoning in the blender and blend on medium speed until lightened. With the motor running, slowly add the melted butter to the blender, leaving the solids in the pan. Increase the blender speed to high for a few seconds to thoroughly combine. Add a little bit of hot water to thin the sauce to a nice, spoonable consistency. Set the blender canister by the stove to keep warm.
For the eggs: Fill a wide, shallow pot with about 3 inches of water. Bring to a brisk simmer and add the vinegar. Crack 4 of the eggs into separate small bowls or ramekins, then gently slide the eggs into the simmering water. Cook at a gentle simmer until the whites are set but the yolks are still runny, 2 to 3 minutes. Gently remove the eggs from the water with a slotted spoon or spider and place on a paper towel-lined plate to drain. Repeat with the remaining 4 eggs.
Put 2 tomato slices onto each of 4 plates and top each tomato slice with a slice of ham and a poached egg. Spoon the hollandaise on top, sprinkle with the scallions and serve immediately.