Place the softened cream cheese and coconut yogurt into a large mixing bowl. Using a hand mixer on low speed or a sturdy whisk, mix them together slowly until the mixture becomes completely smooth and creamy. Take your time at this stage, scraping down the sides and bottom of the bowl as needed, to ensure there are no lumps left. A smooth base here is key to achieving a silky cheesecake texture later.

Add the powdered low-carb sweetener and vanilla extract to the bowl. Mix gently until everything is evenly blended. Pause to taste the mixture and check the sweetness, keeping in mind that the flavors will mellow slightly once the cheesecake is chilled. Adjust sweetness if needed, but aim for a balanced, lightly sweet flavor rather than an overpowering one.

With the mixer on low speed, slowly drizzle in the melted coconut oil or softened butter. Pouring it in gradually helps it blend smoothly into the mixture without separating. Continue mixing just until the fat is fully incorporated and the filling looks glossy and cohesive. Avoid overmixing, as too much air can affect how the cheesecake sets.

Pour the finished cheesecake mixture into the prepared pan. Use a spatula to spread it evenly, gently pushing the filling into the edges and smoothing the top. Lightly tap the pan on the counter once or twice to release any trapped air bubbles, then smooth the surface again for a clean, even finish.

Place the pan into the refrigerator and let the cheesecake chill undisturbed until fully set. This usually takes several hours, and allowing enough time is important for the best texture. Once firm, remove the cheesecake from the pan, slice into portions, and serve chilled for a creamy, refreshing, and perfectly set no-bake dessert.