Using a three-inch ring mold, cut out four pieces of cooked polenta.
In a nonstick skillet over medium heat, cook polenta in oil until browned and crisp, flip and cook other side, approximately five minutes a side. Set aside and keep warm.
Return skillet to heat. Grease inside of 4 ring molds with oil. Place ring molds into the skillet and crack egg into each mold. Cover and cook on low heat until egg white is fully cooked and yolk is beginning to thicken.
While eggs are cooking, heat ham in skillet until heated throughout.
To assemble, spoon Hollandaise on plate, stack crisp polenta, ham, egg and garnish with arugula.
In medium saucepan over medium-high heat, sauté onion in olive oil until translucent. Stir in chicken stock and polenta. Reduce heat to medium. Cook, stirring frequently until polenta is soft and creamy.
Pour cooked polenta into a nonstick baking pan. Use metal spatula to spread 1-inch thick.
In small saucepan over medium heat, add wine, vinegar and shallots. Cook and reduce by half, strain and set liquid aside.
Beat together yolks in large stainless steel mixing bowl.
Add reduced wine mixture to egg yolks. Place bowl over pot of simmering water. Whisk the eggs vigorously until pale and thick enough to come off the side of the bowl and mixture has reached at least 160° F.
Remove from heat and add melted butter slowly until fully incorporated.
Add lemon juice, cayenne, salt and cracked pepper.