Gently warm your pumpkin ale or apple cider to about 100°F, checking with a thermometer so it doesn't get too hot. Turn your oven on to 425°F so it's fully preheated by the time your dough is ready to bake.
In the bowl of a stand mixer fitted with the dough hook, combine 1 ½ cups of the flour with the sugar, yeast, turmeric, and salt. Stir them together with a fork just until evenly distributed.
Pour in the warmed liquid and mix on low speed until everything is well blended. Slowly add the remaining ½ cup of flour while the mixer runs, until the dough pulls away from the bowl and forms a ball.
Turn the dough out onto a floured surface and knead it for about 3 minutes, adding a little more flour if it feels sticky. Cut the dough into 4 equal pieces and shape each one into a ball.
Use a rolling pin to shape each ball into a thin flatbread, then transfer them to your prepared pan. Brush with olive oil and scatter on the apple, sausage, thyme, red onion, and half of the Asiago shavings.
Slide the flatbreads into the oven for about 10 minutes, or until the crust looks fully cooked through. Pull them out, sprinkle over the remaining Asiago, and finish with a generous drizzle of hot honey before serving.