Cut the peeled ube into chunks and place in a steamer basket over simmering water. Cover and steam for about 20 minutes, or until the ube is very tender when pierced with a fork.

Remove the ube from the steamer and let it cool to room temperature. Mash until very smooth or blend in a food processor to form a smooth purée.

Measure 1 cup of the ube purée and add it to a blender. Pour in 3/4 cup of the whole milk, the coconut milk, and the white sugar. Blend until the mixture is completely smooth and evenly colored.

In a small saucepan, pour the remaining 3/4 cup whole milk and sprinkle the unflavored agar-agar powder evenly over the top. Let it sit for 5 minutes to allow the agar-agar to bloom.

Place the saucepan over medium-low heat and cook, stirring constantly, until the agar-agar is fully dissolved and the mixture is smooth and steaming, about 3 to 5 minutes. Do not let it boil.

Pour the blended ube mixture into the saucepan with the hot agar-agar mixture while stirring. Continue to cook over medium heat, stirring occasionally, until the mixture is hot and steam rises, 3 to 5 minutes, without letting it boil.

Remove the saucepan from the heat and skim off any foam if needed. Carefully pour the mixture into 4 small glasses, ramekins, or molds, dividing it evenly.

Let the filled containers cool at room temperature for 15 to 20 minutes, then transfer them to the refrigerator. Chill for at least 3 hours, or until fully set and gently wobbly.

Serve the panna cotta chilled directly in the cups, or run a thin knife around the edges and unmold onto plates before serving.