In a medium saucepan, off the heat, whisk together the brown sugar and cornstarch until smooth and lump-free.

Slowly pour in about 1/2 cup of the milk while whisking to create a smooth paste.

Once it is lump-free, whisk in the remaining milk until fully combined.

Place the saucepan over medium heat. Cook while whisking constantly until the mixture begins to steam and thickens to a pudding-like consistency, about 5 to 8 minutes.

Once thick, reduce heat to low and cook for an additional 1 to 2 minutes while still whisking.

Remove from heat and stir in the butter and optional salt and vanilla until the butter is melted and the pudding is glossy and smooth.

Taste the mixture and adjust the sweetness if needed.

Pour the pudding into 4 small bowls. Press plastic wrap onto the surface to avoid a skin from forming.

Let it cool at room temperature for 15 to 20 minutes, then refrigerate for at least 2 hours until fully set and cold.