Preheat the oven to 210°C. Prepare 15 pieces of muffin liners.
Rub lemon zest and sugars with fingers. Melt the butter and mix it with sugars and lemon zest. Mix until fully combined. You should end up with small crumbles.
Add eggs, oil, vanilla extract, and thick yogurt with lemon juice. Mix for a few minutes (2-3 minutes) but don't overmix.
Add flour, salt, and baking powder. Mix with an egg whisker or until the flour disappears. The batter should be very thick. Add poppy seeds.
For the crumble topping - mix oil, flour, lemon juice, and sugar in a bowl. If it's too dry, add more oil. If it's too moist, add flour.
Put muffin liners into every second "muffin hole" for the maximum rise. Scoop batter into muffin liners (an ice cream scoop works well for this), filling about ¾ of the way. Sprinkle crumble topping over the batter all the way to the top.
Bake for 5 minutes. Lower the temperature to 180°C and bake for additional 11 minutes or until the toothpick comes out clean.
Take the muffins out of the oven and let cool in the muffin tin for 15 minutes. Then let them out and let them cool completely.
For the lemon icing - mix the icing sugar with lemon juice. This one is tricky - you need the mixture to be thick as the American pancake mix. So if it's too runny, add more icing sugar. If it's too thick, add lemon juice. Drizzle some over the muffin tops.