Rinse artichoke bottoms and place in a saucepot. Cover with 1-inch lightly salted water. (If using fresh artichokes, add juice from half a lemon). Simmer 5 to 10 minutes or until artichokes are tender but not overcooked (fresh artichokes will take longer to cook). While artichokes are cooking, add butter to a warmed pot over medium heat. Add flour and whisk briskly, fully incorporating flour with butter. Let cook for 1 minute, whisking all the while. Whisk in milk. Let mixture come to a gentle boil, then reduce to a simmer, whisking frequently. Let simmer 5 minutes. Add salt, pepper and Tabasco to taste. Stir in spinach leaves, 1 cup at a time, allowing to wilt before adding next cup. Stir in minced ham.
When ready to serve, poach eggs: into a pot of salted boiling water with a tablespoon of white vinegar added, gently break 4 eggs at a time and let simmer until whites are cooked through. Remove carefully with a slotted spoon and let drain on a paper-towel-lined plate. Place two drained artichoke bottoms on each plate. Spoon creamed spinach over artichokes. Place 1 poached egg in each artichoke, and top with a spoonful of Hollandaise Sauce.