Use your preferred method to cook the squash (see notes).
Make the dough. Weight both flours in a large bowl and combine turmeric powder with aquafaba in a small jug. Pour the aquafaba mixture over the flours to form the dough. Add more water if required, and work the dough until smooth. Cover with cling film and let it rest for 30 minutes.
Meanwhile make the filling by combining mashed squash pulp with the remaining ingredients. Transfer into a piping bag.
Shape the ravioli. Roll out the dough, either by hand using a rolling pin, or with a pasta machine. Make sure to roll it into very thin sheets before shaping the ravioli (thickness 2-3 if using the pasta machine). Make sure to dust the working surface (or bottom of the mould) before placing the sheet of pasta over.
Pipe the filling, then run a slightly damp finger around it (or on the ravioli junctions) to better seal the second layer of pasta. Gently cover with another pasta sheet, making sure not to form any air bubbles in between the two doughs. (see post for detailed method for mould or cutter versions)
Place the ravioli onto a floured surface to prevent them to stick to the bottom. Do not overlap.
For the thyme infused white sauce: heat the milk with a bunch of thyme. Reduce the heat and simmer for 5 minutes. Combine flour and oil into a paste, then carefully add a splash of thyme infused milk at the time, to avoid lumps. Season with salt and put back on gentle heat until the sauce thickens (3 to 5 minutes) stirring all the time.
Cook the ravioli in plenty of salted boiling water then transfer into the pan with the thyme infused sauce. Please note: cooking time varies based upon the thickness of the pasta, but it normally takes 1 to 3 minutes to cook fresh ravioli. Make sure to save some of the cooking water.
Coat the ravioli in the white sauce, add around ½ cup of cooking water to loose up the sauce, then heat for 30 seconds to 1 minute.
Garnish with fresh thyme and freshly ground pepper and serve.