Created by ForeverMama on December 7, 2019
Step 1: Melt the butter in a small saucepan. Stir in the flour. Cook over medium-high heat for 1 minute, stirring constantly.
Step 2: Whisk in the chicken broth and heavy cream. Cook until the sauce is thickened and bubbly, whisking constantly.
Step 3: Stir in the cheese; cook until the cheese melts, whisking constantly. Remove from the heat and cover to keep warm.
Step 4: Arrange the buttered muffin halves on a baking sheet. Top each with a slice of smoked ham. Broil 3 inches from the heat source for 2 minutes; keep warm.
Step 5: Bring 4 inches of water (or enough to cover the eggs) along with the chicken bouillon to a boil in a large skillet. Reduce the heat to medium-high. Crack the eggs 1 at a time onto a small plate; slide each egg into the simmering water. Cook for 4 - 6 minutes, until eggs are cooked with yolk still runny to desired consistency.
Step 6: Remove the eggs with a slotted spoon and dab excess water with a paper towel.
Step 7: Place 1 egg on top of each ham-topped muffin half. Spoon the cheese sauce over and sprinkle with pepper.