Preheat oven to 450° and place a large baking sheet in the oven.
In a small bowl, whisk together oat milk and yogurt. Place in fridge to chill. Combine flour, sea salt, baking powder, baking soda and sugar in a food processor. Pulse a few times to fluff up the mixture. Add cheese, garlic, chives and dill, if using. Pulse a few more times to incorporate.
Roughly chop shortening and butter and add to food processor. Pulse ingredients until pieces of butter and shortening are pea-sized. Do not pulse too much! Transfer mixture to a bowl.
Create a well in the dough and add chilled oat milk and yogurt mixture. Using a large fork, gently incorporate the dry into the wet. If there are any large chunks, use the fork to break them up.
Transfer dough to a flour-dusted surface. Press with your hands a couple of times to combine the dough and further incorporate. Pat into a 2-inch thick square.
Using a sharp and flour-dusted knife, cut dough into 4 pieces. Stack pieces on top of one another, press down to flatten. Pat dough into a 2-inch thick square. Repeat this step. Using the floured-knife, trim a thin border around sides of dough to create clean edges. Cut into 9 biscuits.
Carefully, remove the heated pan out of the oven and line with parchment paper. Transfer the biscuits to the pan, leaving a few inches of space in between. Brush the tops with melted butter and bake for 25 minutes, until golden brown.