Step 1

Preheat oven to 425° F. On a rimmed baking pan, arrange asparagus in a single layer. Drizzle with olive oil and sprinkle with 1/4 teaspoon each salt and pepper. Roast 10 to 12 minutes or until asparagus is tender.

Step 2

In small saucepan, heat cream over medium-high heat until just simmering. Reduce heat to medium and simmer 6 to 8 minutes or until cream is reduced to 1/2 cup, or is a thickened, saucy consistency. Remove from heat; whisk in lemon juice, butter, tarragon, lemon zest, mustard powder, and remaining 1/8 teaspoon each salt and pepper. Keep in a warm spot on your stove.

Step 3

Fill a high-sided skillet with water; heat to boiling over high heat. Reduce heat so that water is just barely bubbling. Add vinegar to water. Crack each egg into a small bowl or ramekin and slide egg into water. Poach 3 to 4 minutes or until whites are cooked through but yolk is still soft. Remove eggs from pan and drain on paper towel.

Step 4

Divide asparagus between plates. Top with poached eggs and drizzle with sauce; garnish with additional tarragon.