Grease and line an 8x8 pan with parchment paper, with two sides overhanging to use as handles. In a large saucepan, bring chicken (or veggie) broth and milk to a boil. Once boiling, turn heat down to medium. Slowly add polenta into saucepan, whisking constantly. Reduce heat immediately to medium-low or low, continuing to whisk almost constantly until thick and creamy, about 7-8 minutes. You'll want a lower heat that keeps it from splattering.
Remove from heat and add butter, nutritional yeast, thyme, and salt and pepper to taste. Stir to combine. Transfer to prepared pan. Press polenta into an even layer and smooth top with a spatula. An extra piece of parchment is helpful in pressing polenta into pan.
Refrigerate for two hours or overnight. When ready to bake, preheat oven to 450 degrees Fahrenheit. Gently lift out slab of polenta using parchment handles and transfer to cutting board. Slice polenta into 18 (4 x 1-inch) strips and place onto a greased baking sheet. Brush each strip with olive oil and sprinkle with salt.
Bake for 15 minutes, carefully flip over strips, and bake for about 10 to 15 minutes more or until crispy and browned on the edges.
While the polenta fries are baking, combine the Cajun Aioli ingredients in a small bowl. Stir to combine. Refrigerate until ready to serve with polenta fries.