Preheat oven to 400°F. Grease an 8 x 4-inch loaf pan with 1 tablespoon avocado oil, then line it with parchment paper.
In a small bowl, mix rolled oats, thyme, pumpkin seeds, and caraway seeds.
In a separate large bowl, whisk together all-purpose flour, whole wheat flour, baking powder, baking soda, and kosher salt.
Add the grated beet and all but 1 tablespoon of the oat and seed mix to the flour mixture. Do not stir; just set aside.
In another bowl, whisk eggs, avocado oil, sour cream, honey, and Parmesan cheese until combined. Pour this wet mixture over the flour and beet mixture.
Using a spatula, gently fold the mixture together until just combined. Carefully fold in the goat cheese, trying to keep it in small pieces.
Transfer the batter evenly into the prepared loaf pan. Sprinkle the reserved 1 tablespoon oat and seed mix evenly over the top.
Bake for 40 minutes, then cover tightly with foil and bake for another 40 minutes.
Remove from oven and let cool in pan for 5 minutes. Turn out onto a wire rack and invert so the seed side is up. The crust should be crisp and dark.
Cool completely for at least 20 minutes before slicing.