Finely crush cookies in a food processor.: The aroma of crushed cookie is the first sensory clue that you are on the right track, it should smell rich and slightly toasty, and the crumbs should look uniform like coarse sand rather than large chunks. This texture helps the crumbs compact evenly when mixed with melted butter , so stop pulsing once no big pieces remain. A common mistake at this stage is over processing into powder which makes the crust feel too dense, so pulse in short bursts and check frequently. If your processor leaves a few visible bits, that is fine, they add pleasant crunch in the finished crust.
Combine cookie crumbs and melted butter. Press into the bottom and up the sides of a springform pan.: You will notice the crushed cookie absorb the glossy melted butter , turning from dry crumbs into a tacky mixture that holds together when squeezed. Press it firmly into the base and about one inch up the sides to create a sturdy cradle for the filling; use the base of a glass or measuring cup to compact the crumbs evenly. The smell will be warm and buttery, and the visual should be a smooth, even layer. Avoid pressing too thin or unevenly, because thin spots can lead to a soggy bottom, while overpacking can make the crust too hard to slice cleanly.
Puree 2 cups of peach slices in food processor until smooth. Set aside.: The pureed peach should be silky and brightly colored, releasing a fragrant, fruity perfume as you blend. This puree is the core flavor base, so taste it and adjust mentally for ripeness; if the peaches are mild, the final pie will be milder. Strain only if there are tough fibrous pieces, but I usually keep everything for maximum peach character. A typical slip is under blending, leaving stringy bits that affect texture in the smooth filling, so blend until it is uniformly smooth and vibrant.
Whip heavy cream until stiff peaks. Fold in sweetened condensed milk, peach puree, and vanilla.: As you whip the heavy whipping cream , watch for it to move from glossy soft peaks to firm, holdable peaks; this is both a visual and tactile cue, you should be able to lift the whisk and see the peak hold its shape. Folding in the sweetened condensed milk , peach puree, and vanilla should be done gently to preserve the aeration, using a large spatula in sweeping motions. The mixture will smell like fresh peach and rich dairy, and look pale peach with light billowy texture. If you stir too aggressively you will deflate the cream and the filling may freeze denser instead of light; fold slowly and stop as soon as the mixture is homogenous.
Chop the remaining cup of peach slices. Fold into heavy cream mixture.: The chopped peach pieces add delightful bursts of texture against the creamy filling. They should be uniformly sized so each spoonful has a pleasant balance between smooth and fruity chew. Gently fold them in so they remain distinct pockets rather than breaking down completely into the base. Watch for excess juice from very ripe fruit, blot with a paper towel if necessary, because excess liquid can form icy pockets in the finished pie.
Spread ice cream into cookie crust. Cover with plastic wrap and place in freezer. Freeze for 6 hours, or until set.: When you spoon the filling into the prepared crust, the contrast of the pale peach filling against the golden rim is an encouraging visual cue, and the filling will feel cool and luscious as you level it. Smooth the surface with a spatula, then cover closely with plastic to prevent ice crystals, and set the pan on a flat shelf in the freezer. The six hour freeze yields a firm, scoopable texture; if you disturb it too early it can become uneven or slushy. A common pitfall is placing it near the freezer door where temperature fluctuates, which can lead to frost formation and a grainy texture, so choose the coldest, most stable spot for resting.