Stir together all dry ingredients in a medium sized bowl. In a larger bowl, whisk together the eggs, yogurt, brown sugar, oil and vanilla until smooth. Pour the dry ingredients into the wet and stir until half combined. Add the grated carrot and stir until all ingredients are incorporated. Avoid over-mixing - the batter will be thick! Spread evenly into the prepared loaf pan.
In another medium sized bowl, combine the flour, brown sugar and cinnamon for the streusel. Add the pieces of cold butter and use a fork to cut the butter into the mixture until it forms coarse crumbs. Sprinkle evenly on top of the loaf.
Bake for 45-55 minutes - your loaf is done if you poke the centre with a knife and it comes out clean!
Allow to cool in the pan before removing to slice + serve! Cover and store leftovers at room temperature or 2 days. This loaf also freezes well!
Optional: feel free to add in 1/2-1 cup crushed and drained pineapple, chopped walnuts, shredded coconut or raisins for extra pizazz.