Preheat oven to 170°C (340°F). Grease and line a standard loaf pan with parchment paper.
In a large bowl, rub the white sugar, brown sugar, lemon zest, and cardamom powder together with your fingers until fragrant.
Whisk in the eggs, vanilla extract, vegetable oil, and Greek yogurt until smooth and well combined.
In a separate bowl, whisk together the all-purpose flour, rye flour, baking soda, salt, and cinnamon.
Gently fold the dry ingredients into the wet mixture until just combined. Fold in the grated carrots and grated apples.
Pour batter into the prepared loaf pan and smooth the top. Bake for 70 to 80 minutes at 170°C until a skewer inserted in the center comes out clean. Cool in pan for 20 minutes, then transfer to a wire rack.
To make the glaze, melt the butter and brown sugar in a saucepan over medium heat until bubbling.
Whisk in heavy cream, coffee mixture, and a pinch of salt. Simmer for 2–3 minutes until smooth, then stir in chopped walnuts and remove from heat.
Pour the warm walnut coffee toffee glaze over the cooled loaf cake before slicing and serving.