Preheat the oven to 425 degrees F. Line a sheet pan with parchment paper.
Add the green olives, kalamata olives, giardiniera, capers, parsley, vinegar, olive oil and honey to a food processor and pulse to make a coarse relish.
Slice the boule in half horizontally. Spread the tapenade evenly over both halves of the boule. Layer the cheese evenly over the tapenade on the bottom half of the boule. Place both top and bottom halves cut-side up beside each other on the sheet pan.
Lay the hot hash browns on top of the cheese, then evenly pile on the corned beef. Bake the open sandwich until the cheese is melted and the corned beef is warmed through, 6 to 8 minutes.
Melt the butter in a large nonstick skillet over low heat. Working with one egg at a time, crack each egg into a small bowl or ramekin and then slowly add it to the skillet. Cover with a tight-fitting lid and cook, uninterrupted, until the whites are set but the yolks are still runny, 2 to 2 1/2 minutes. Season the eggs with pepper. Slide the eggs onto a plate.
Top the corned beef with the sunny-side up eggs. Place the top piece of bread onto the sandwich. Cut into 4 wedges and serve.