For the crumble topping:

1. In a medium bowl, stir together flour and sugar. 
2. Add cold butter pieces and work with your hands or a pastry cutter to integrate. The mixture will be crumbly, irregular, with butter pieces the size of peas and beans. 
3. Refrigerate while making the muffin batter. 

For the apple muffins:

1. Preheat the oven to 350ºF / 180ºC.
2. Line 6 jumbo muffin pan or 12 regular muffin tins with paper liners or butter/spray the pans. 
3. In a large bowl sift together the dry ingredients: flour, baking powder, salt, both sugars and apple spice. Stir to combine.
4. Whisk eggs, milk, oil, and vanilla in a medium bowl. Do not beat but mix well until no streaks of egg whites remain.
5. Add the wet ingredients at once to the bowl with the dry ingredients.
6. Mix until you barely have streaks of flour, but do NOT overmix. It will be lumpy and not completely mixed and that is fine.
7. Add the diced apples and stir lightly to combine with a rubber spatula.
8. Divide the apple muffin batter evenly among the prepared muffin cups or liners. Don't go over 3/4 of their capacity. 
9. Sprinkle with the streusel topping. You might not use it all. 
10. Bake for 25-30 minutes, until the top is dry and golden brown, and a cake tester or toothpick inserted in the center comes out clean. Don't overbake.
11. Let cool down completely before glazing. Or eat warm without glaze. 
12. They are best eaten the day they are made, but you can keep them for a day at room temperature covered or wrapped.
13. Store leftovers, covered in plastic wrap or in an airtight container, in the refrigerator for a few days or frozen for a month. 

For the lemon glaze:

1. Mix powdered sugar with juice in a small bowl until smooth and creamy. It should be like thick honey. If needed add more lemon juice, 1/2 teaspoon at a time until you reach the desired consistency. 
2. Drizzle over the cooled muffins and let dry before serving.