Cut the potatoes into bite-sized pieces that are 2 cm thick (3/4 inch), then add the chopped potatoes into a stockpot, all in a flat layer, and fill with water, just enough to barely cover the potatoes, season generously with salt, and heat with a high heat

In the meantime, heat a large fry pan with a medium heat and add in the olive oil

After a couple of minutes, add in the chopped onion and garlic, mix continuously, after 3 minutes and the onions are slightly translucent, add in the flour and continue to mix together for 2 minutes, then add in the milk, vegetable broth, saffron, and thyme, and gently mix together until you get a slightly creamy sauce

Once you end up with a slightly creamy sauce, about 4 to 5 minutes, season with salt & pepper, and mix together, then lower to a low heat and simmer

About 15 to 20 minutes after turning on the heat on the potatoes, they should be just cooked through; you can always pierce them with a toothpick to ensure they are done, you kind of want them al dente, at this point, using a large slotted spoon, transfer the potatoes directly from the stockpot to the pan with the simmering cream sauce, and it's ok if a little of the starchy potato water goes into the sauce

Turn off the heat on the pan, add the grated cheese over the potatoes and lemon juice, gently mix together until well mixed, transfer into a large serving dish, and top off with chopped parsley, enjoy!