Place a sieve lined with a double layer of muslin cloth over a bowl. Add the yoghurt, fold up the sides of the cloth and twist to tighten. Secure with a rubber band and chill overnight to drain liquid.
When ready to serve, combine smoked paprika, chilli, mint and salt in a small bowl. Add melted butter and lemon juice, stirring to avoid lumps. Add lentils and stir to combine.
Toast bread to your desired level. Meanwhile, bring a large pot of water to the boil. Reduce heat to low and gently crack in your eggs. You may need to cook in two batches to avoid overcrowding. Cook on low heat for 4 minutes or until cooked to your desired yolk consistency.
Remove labneh from muslin cloth and transfer to a bowl. Discard liquid in the bowl under the sieve.
Spread each slice of toast generously with labneh. Top each with a poached egg, followed by marinated lentils (drizzle over marinating juices). Garnish with fresh mint.