Peel, trim, and thinly slice <quantity>1</quantity> carrot

Transfer the carrot to a saucepan and cover with water

Cook over medium-low heat until the carrot is extremely soft

Fill a saucepan half way with water and bring to a boil over medium-high heat

Strain the carrot slices and refrigerate to cool

Carefully add <quantity>3</quantity> eggs to the boiling water and cook for 4m until soft-boiled. Transfer to a bowl with cold water

Halve <quantity>1</quantity> lemon and squeeze the juice into a bowl

Add <quantity>1<unit>tbsp</unit></quantity> of saffron, stir, and set the bowl aside for 10m to infuse the flavors

Peel the eggs and rinse them in water to remove any remaining eggshell

Add the carrot slices and <quantity>1<unit>tsp</unit></quantity> of sweet paprika to a tall container

Add salt to taste and the saffron with lemon mix

Add <quantity>1</quantity> garlic clove and <quantity>3</quantity> of the poached eggs

Mix with an immersion blender on high speed until completely smooth

Add <quantity>300<unit>ml</unit></quantity> of vegetable oil in a thin stream, while blending, to emulsify. Adjust the salt if needed. The rouille purée is ready

Enjoy! This lovely purée pairs perfectly with trout or other kinds of fish!