Bloom the yeast. In a small bowl, combine the warm whole milk, active dry yeast, and 1g sugar. Stir gently and let sit for 5 to 10 minutes until foamy. If the mixture does not foam your yeast is no longer active and you should start with a fresh packet before continuing.
Warm the Greek yogurt. Microwave the nonfat Greek yogurt for 30 to 40 seconds until slightly warm to the touch. Do not overheat. Warm yogurt keeps the yeast active and speeds up the rise.
Combine wet ingredients. In the bowl of a stand mixer fitted with the dough hook, combine the bloomed yeast mixture, warmed Greek yogurt, eggs, granulated sugar, and vanilla extract. Mix briefly on low to combine.
Add dry ingredients. In a separate bowl, whisk together the bread flour, fine sea salt, and ground cinnamon. Add the dry ingredients to the wet ingredients and mix on low speed until a shaggy dough forms, about 2 minutes.
Add the butter. With the mixer running on low, add the softened butter one tablespoon at a time, waiting for each addition to be fully incorporated before adding the next. This slow addition prevents the dough from becoming greasy.
Knead. Once all the butter is incorporated, increase to medium low speed and knead for 6 to 8 minutes until the dough is smooth, elastic, and pulls away cleanly from the sides of the bowl. The dough will be on the tacky side and that is completely normal. Do not add flour unless the dough is still actively sticking to the sides of the bowl after the full knead. Only add bread flour 10 grams at a time if needed.
Bulk rise. Shape the dough into a smooth ball and place in a lightly oiled bowl. Cover and let rise at room temperature for 1 to 1.5 hours until doubled in size. In a warm kitchen at 75 to 80 degrees F this happens closer to 1 hour. A cooler kitchen will take longer. Watch the dough, not the clock.
Divide and shape. Turn the dough out onto a lightly floured surface. For ring donuts, gently roll the dough to 3/4 inch thickness using a lightly floured rolling pin and cut rounds using a 2.5 to 3 inch cutter. Use a 1 inch cutter to cut the center holes. For solid rounds, divide the dough into portions and roll each into a tight smooth ball. Place each shaped donut on its own small square of parchment paper.
Second proof. Cover loosely and proof at room temperature for 45 minutes to 1 hour until visibly puffed. If your kitchen runs cool, place the sheet pan in the oven with just the light on. The donuts are ready when they look puffy and pass the float test.
Float test. Before frying the whole batch, lower one donut into the oil. If it floats immediately the rest are ready. If it sinks, give the batch another 15 minutes and test again.
Heat the oil. Pour avocado oil into a heavy bottomed pot or Dutch oven to a depth of 2 to 3 inches. Heat to 350 degrees F using an instant read thermometer to monitor temperature.
Fry the donuts. Lower each donut into the oil parchment side down using tongs. Within about 30 seconds the parchment will release on its own and can be removed with tongs. Fry 2 to 3 donuts at a time. Do not crowd the pot. Fry for 1 minute 20 seconds to 1 minute 30 seconds per side until deep golden brown. Transfer to a wire rack or paper towel lined sheet to drain. Check oil temperature between batches and let it return to 350 degrees F before adding the next round.
Make the chocolate glaze. Whisk the powdered sugar and cocoa powder together first to remove lumps. Add the melted butter, vanilla extract, and pinch of salt. Whisk in the whole milk one tablespoon at a time until smooth and glossy.
Make the vanilla glaze. Whisk the powdered sugar, vanilla extract, salt, and whole milk together until smooth and pourable. Add milk gradually until it coats the back of a spoon.
Glaze the donuts. Let the donuts rest for 3 to 5 minutes after frying before dipping. Dip the top of each donut into the glaze of your choice and let the excess drip off. Set on a wire rack. Add sprinkles or toppings immediately before the glaze sets. The glaze will begin to set and harden within about 5 minutes.