Make the pralines: Melt 1 tablespoon butter in a medium heavy saucepan over medium-low heat.
Add the remaining 3 tablespoons butter, granulated sugar, brown sugar, and half-and-half; stir until the butter is melted and the sugars dissolve.
Stir in the chopped almonds, then increase heat to medium and bring the mixture to a boil.
Cook, stirring occasionally, until a candy thermometer reaches 238°F (soft-ball stage), about several minutes.
Remove from heat and stir in the vanilla and almond extract; continue stirring 2–3 minutes until slightly thickened.
Drop the praline mixture by heaping teaspoons onto a parchment-lined baking sheet; let cool until set.
Prepare the milkshakes: Scoop the vanilla ice cream into a blender.
Add the almond paste, the cooled pralines (or praline candies), and the milk to the blender; blend on medium-low until smooth.
If needed, add a little more milk to reach your desired consistency, then divide the milkshake among chilled glasses.
Top each milkshake with a dollop of whipped cream and a sprinkle of coarsely chopped almonds, if desired.