Stir milk, pumpkin, sugar, and pumpkin pie spice for milk base together in a saucepan over medium-high heat. Cook, stirring, until sugar dissolves and mixture just comes to a simmer. Remove from heat, stir in coffee liqueur, and cover to keep warm.
Stir boiling water, instant coffee, sugar, and pumpkin pie spice for whipped coffee together in a bowl. Beat with an electric mixer on high until fluffy and stiff peaks form, about 2 minutes.
Divide warm milk base between 2 large mugs. Top with whipped coffee.
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