Place the milk chocolate in a medium bowl. Pour the cream into a small saucepan and bring to a boil over medium heat. Pour the hot cream all at once on top of the milk chocolate. Let sit for 1 minute, then whisk until smooth. Strain into a bowl, cover with plastic wrap, and puncture several holes in it with the tip of a paring knife. Refrigerate for at least 4 hours, or overnight.
To make the caramel, combine the cream and butter in a small saucepan, and heat over low heat, stirring occasionally, until the butter melts. Remove from the heat.
Meanwhile, put the sugar in a large saucepan, and heat over low heat until the sugar melts and turns into a sheet of golden caramel.
Immediately whisk the hot cream mixture into the caramelized sugar. The mixture will boil and rise up in the pot. Turn the heat off, and whisk until any hardened pieces of caramel dissolve. Strain into a bowl, and refrigerate for at least 1 hour, until just semisoft.
Divide the caramel among the tart shells, spreading it into a 2-inch circle in the center of each one. Set aside.
Pour the chilled milk chocolate cream into the bowl of a stand mixer or a medium mixing bowl. Using the whisk attachment or a hand-held mixer, beat at medium speed until medium to firm peaks begin to form. Spoon the whipped chocolate cream into the tarts. Gently shake the tarts to level the tops. Refrigerate for 10 minutes.
Fill a small paper pastry bag with the melted chocolate. Stripe and dot the top of each tart. Let sit for 5 to 10 minutes.