Place the eggs in a large saucepan and cover them with water. Bring the water to a boil, then remove the saucepan from the heat. Leave to stand, covered for 12 minutes.

Place the eggs in a colander and rinse with cold water to stop the cooking process. Let the eggs cool down for a few minutes, then peel and halve them.

Melt the butter in a saucepan large enough to hold all the eggs in the end.

Sprinkle the flour in the saucepan and stir well for about 1 -2 minutes until the flour becomes a bit yellow, but doesn't get too dark.

Start adding the vegetable broth, little by little, whisking constantly to avoid your sauce getting clumpy. In the end, the mixture should be very smooth.

Add the heavy cream, bring to a boil, and cook, stirring very often, until the sauce thickens and coats the back of a wooden spoon. That should take about 5 to 8 minutes.

Add the mustard, lemon juice, sugar, and dill, and stir well. Adjust the taste with salt, white pepper, and more lemon juice or sugar if necessary.

Place the egg halves in the saucepan, stir very gently to cover with sauce, and heat through for a few minutes.

Serve immediately with boiled potatoes and green salad.