Peel and finely dice the carrots and onion. Peel the shallots and quarter them lengthwise. Wash herbs and shake dry. Cut bacon into small cubes
Melt butter in a pot. Fry the bacon, carrots and diced onion for about 2 minutes. Add flour and sweat for 1-2 minutes. Deglaze with 100 ml water and wine. Add tarragon, parsley and thyme, except for 4 stems for garnishing, tie together with kitchen string and add to the pot. Season with salt and pepper. Simmer at low heat for about 30 minutes
In the meantime, heat 400 ml water with vinegar in a small pot until just before boiling. Put 1 egg in a small bowl. Use a whisk to create a whirl in the water. Add the egg from the shell to the strudel and poach for 2-3 minutes. Lift the egg out of the pot with a skimmer and drain on kitchen paper. Poach the rest of the eggs in the same way. Line a baking tray with a damp tea towel. Place eggs on top and cover with another damp cloth. Keep warm in a preheated oven (electric cooker: 50 °C/ circulating air: 35 °C/ gas: see manufacturer)
Remove the herb bouquet from the sauce. Season the sauce with salt, sugar and pepper. Arrange sauce with eggs on plates and garnish with thyme stems