Pre-heat the oven to 180°C (360°F) with fan. Line a large baking tray with baking paper (parchment).
In a bowl add the milk, instant yeast and 1 teaspoon of sugar. Mix and let it bloom for 5-10 minutes until bubbles form on the surface.
Place the melted butter (cooled to room temp), eggs and yeasty mixture in a large bowl. Add the flour and the rest of the sugar and mix everything with a wooden spoon until a dough forms.
Put the dough on the work surface and knead it by hand for 4-5 minutes or until the dough is no longer sticky. Do not add any additional flour while kneading. Once smooth, place the dough in a large bowl greased with oil, then cover with plastic film. Let it prove in a warm place for 30-45 minutes or until it doubles in volume.
Prep the metal pastry cones by brushing them with butter. Once the dough has proved, divide it into 8 equal parts. Roll out each part of dough into a thin strip roughly 40 cm (15 inches) in length.
Spin the strip of dough around a metal cone, ensuring each roll overlaps the pervious one slightly. gently press the dough with your fingers to ensure it sticks together.
Brush with egg yolk mixed with 1 teaspoon of milk. Optional: add in a little orange food colouring into the egg yolk to make the cones more 'carroty'.
Mix the sugar and cinnamon in a bowl, then sprinkle the mixture over the chimney cones. Bake for 20-25 minute or until they start to brown slightly around the edges.
Let them cool on the tray and fill with your favourite frosting or cream before serving.
Add mint leaves on top to create the carrot leaves.
Vanilla pastry cream
In a small saucepan, heat up the milk and vanilla bean paste. The milk should be hot, but just before boiling point.
Whip up the egg yolks with the sugar until pale and fluffy. Add in the cornstarch, then mix until fully incorporated. Add the flour, and mix once more until fully incorporated. Add 1-2 teaspoon of the milk if the mixture becomes too stiff.
Pour half of the hot milk into the eggs, then use a whisk to mix vigorously. Mix really well to prevent any lumps. Strain the mixture back into the saucepan with the remaining milk, then return to the stove.
Cook the pastry cream over low heat, mixing continuously to prevent lumps. Once the mixture has thickened up, remove it from the heat and add in the butter. Whisk well to melt the butter into the cream.
Place the vanilla pastry cream into a shallow bowl, then cover with plastic film. Ensure the plastic is in direct contact with the cream, then let it cool down. Refrigerate for 1-2 hours before using. Once fully chilled, whip it up with a hand mixer to loosen up the pastry cream.
Notes
I recommend using a kitchen scale in grams for more accuracy. The cups used for the conversion are standard US customary cups (1 cup flour = 136g). There are many different types of cups across the globe, which is why I strongly recommend using grams instead.
The chimney cones can also be brushed with melted butter instead of egg yolk.