Combine the yeast, warm water, and 2 tablespoons honey in the bowl of your stand mixer. Let it foam up for about 10 minutes, and then add the oil, milk, egg, egg yolk, salt and 2 cups of the flour. With the dough hook attached, mix the ingredients together on medium speed until the dough starts to come together. Reduce the speed to low, and add the rest of the flour, 1/4 cup at a time, until the dough starts to pull away from the sides of the bowl and wrap around the dough hook. Knead the dough for about 5 minutes until the dough is smooth and elastic. If the dough is too sticky, add more flour until you reach a smooth and elastic consistency.
Turn the dough into a well oiled bowl. Cover the bowl with plastic wrap and place it in a warm place. Let the dough rise for about an hour or two or until doubled in size.
Turn the dough out onto a lightly floured surface. Form the ball into a rectangle and then roll it out until it is 1/4 inch thick. Spread the room temperature butter on top and sprinkle with brown sugar, cinnamon, and cardamom. Roll the dough (lengthwise) tightly into a log. Cut the log into 1-inch slices and place them on two parchment lined baking sheets, spacing them about 2 inches apart. Cover the baking sheets with tea towels and let the buns double in size. This should take about an hour.
Preheat your oven to 350 degrees F and bake the buns for 10-12 minutes or until lightly brown on top. Remove from heat and let cool for 5-10 minutes while you prepare your glaze.
Whisk together the powdered sugar, honey and whole milk. If you find it difficult to get a smooth consistency, your stand mixer with whisk attachment fixed works well for this. Drizzle the glaze on top of the honey buns and serve warm.
The honey buns will store in an airtight container for 1-2 days, but are best served fresh out of the oven.