In a pot, bring chicken stock and milk to a boil. Then whisk in cornmeal until smooth. Turn heat down to medium and cook for another 8-10 minutes, stirring frequently.
Remove from heat and stir in lemon juice, parmesan, thyme, and salt.
Immediately transfer to a parchment-lined rimmed baking tray. Smooth the surface to about a 2-inch thickness. Cover with plastic wrap and chill for about 2 hours to firm up.
Meanwhile make the aioli: blend roasted garlic, lemon juice, egg, salt and pepper and whisk them in a bowl. Slowly add olive oil, whisk until fully emulsified. Chill in the fridge.
Preheat oven to 450F. Slice polenta into strips and place them on a greased baking sheet. Drizzle more olive oil on top and bake for 15 minutes. Flip the polenta fries and continue baking for another 10-15 minutes or until crispy and browned on the edges.