In a nonreactive saucepan, bring the milk, vanilla bean, crushed coffee beans and cardamom to a simmer over medium heat. Immediately turn off the heat and set aside to infuse for 15 minutes. Meanwhile, in a mixer fitted with a whisk attachment (or using a hand mixer), whip the egg yolks, sugar and salt until pale yellow and fluffy. With the mixer running at low speed, mix in the cornstarch, then very gradually pour in the hot milk mixture, mixing it in as you go.

Strain the mixture through a fine sieve back into the saucepan, to smooth it and to remove the spices. Whisking constantly, cook over medium-high heat until thick and just boiling. When the mixture thickens, the whisk will leave trail marks on the bottom of the pot and the mixture will have a few large bubbles boiling up to the top. Cook just until no starchy taste or feeling remains. Remove from the heat and stir in the butter until melted. Pour into 4 custard cups, ramekins, or mugs and chill, uncovered, at least 2 hours or overnight. Serve chilled, placing a whole coffee bean in the center of each serving.