Melt butter in a large skillet over medium heat. Add pears and thyme; cook, stirring often, until pears have softened, about 10 minutes. Crumble Gorgonzola cheese over pears; cook and stir until melted, 2 to 3 minutes. Remove skillet from heat and cool filling completely.
Cut pasta dough into 3 equal pieces. Flatten the first piece of dough on a floured work surface; roll with a rolling pin 5 or 6 times. Turn the dough 45 degrees and roll again, 5 to 6 times. Keep rolling and turning in the same direction until dough has a consistent thickness of about 1/16-inch. Repeat with remaining 2 pieces of pasta dough.
Gently transfer 1 pasta sheet to a floured surface and cut in half to form 2 evenly sized rectangles. Drop about 1 teaspoon filling onto 1 rectangle, spacing the filling about 1-inch apart. Brush the spaces around the filling with water.
Lay the second rectangle on top of the first. Gently squeeze out the air around the filling and press firmly with your hands to seal the edges and all dough around the filling.
Cut square ravioli shapes using a ravioli cutter. Transfer the ravioli to a floured plate or board. Repeat with the remaining dough and filling. Let the ravioli stand for about 30 minutes.
Bring a saucepan of lightly salted water to the boil; gently add ravioli, working in batches. Cook until ravioli float to the top, about 3 minutes. Remove using a slotted spoon and transfer to a warm bowl.
If using a pasta machine:
Take 1 piece of dough and cover the rest in plastic wrap. Flatten the piece between your palms, then pass through the widest setting of your pasta machine. Sprinkle with flour, fold in half lengthways and pass it through the roller again. Repeat 3 to 4 times - always flouring, folding, and passing through the widest setting - until the dough is smooth in texture, no longer sticky, and even in size. Move the pasta machine to a middle setting and pass the dough through again. Move to the next to last setting and pass through again. Cut the pasta sheet in half widthwise. Pass each half through the thinnest and last setting of the pasta machine to obtain two long and very thin sheets.
Gorgonzola and pears is a delicate flavor pairing it's better not to cover with other bold flavors. Simply serve these ravioli with a butter and sage sauce: Melt 1/4 cup butter in a pan and cook 4 to 5 sage leaves for 3 to 4 minutes. Reserve 1 ladle cooking water from the pasta pot, drain the ravioli and transfer to the saucepan. On high heat quickly coat the ravioli in the sauce, adding the cooking water to emulsify the sauce a bit. Scoop onto plates, sprinkle with grated Parmesan, and serve.