For the dill sauce: In a saucepan, bring the heavy cream and dill to a simmer over medium-low heat. Let it simmer until the cream reduces to a thick, smooth consistency. Season with salt and pepper to taste. Once thick, remove from heat. Reheat if necessary.
In a non-stick pan over medium heat, brown the chicken sausage on both sides. Toast the bread.
Heat the oil in a non-stick pan over medium heat. Crack the eggs into the pan. Once the whites of the eggs start to set and become firm, gently flip the eggs over and cook for 1 minute longer. Season with salt and pepper.
Spoon the sauce over the eggs. Serve with toast, chicken sausage, and strawberries.