Bring 4 cups of water to a boil in a medium saucepan with a pinch of salt. (For richer flavor, substitute 1 cup with low-sodium chicken or vegetable stock.)
Gradually whisk in polenta. Reduce heat to low and cook, stirring frequently, until thickened — about 4–5 minutes for instant polenta. Remove from heat.
Stir in olive oil, garlic, thyme, chives, cheddar, and chopped bacon. Season with salt and pepper.
Line an 8x8 baking dish with parchment or lightly oil it. Spread the polenta mixture evenly to about a 1/2-inch thickness and smooth the top.
Chill in the refrigerator for at least 1 hour, or until firm.
Preheat oven to 425°F (220°C). Turn the set polenta onto a cutting board and slice into fry-shaped sticks.
Arrange fries on a parchment-lined baking sheet, spray lightly with nonstick cooking spray (or drizzle a little olive oil), and bake 20–25 minutes, flipping halfway, until golden and crisp.
Meanwhile, mix aioli ingredients: mayonnaise, lemon juice, minced chipotles, smoked paprika, and garlic powder. Taste and adjust lemon or chipotle for preference.
Serve fries hot with chipotle aioli on the side.