Preheat the oven to 350°F (177°C). Melt the butter by placing the butter in an 8x8-inch baking dish and let it melt in the oven. While the butter is melting, in a medium bowl, whisk together the sugar, milk, flour, salt, almond extract, cinnamon, and baking powder until smooth.
Pour the batter from the mixing bowl into the center of the melted butter without stirring. Bake for 25-30 minutes, or until the cobbler is golden brown. Let it cool completely, then break it into bite-sized pieces.
Blend the peaches in a food processor or blender until smooth. In a medium bowl, stir together the peach puree, sweetened condensed milk, lemon juice, almond extract, and sea salt until well combined.
In a large mixing bowl, whip the cold heavy cream until stiff peaks form. Gently fold the peach mixture into the whipped cream until fully incorporated.
Line a 9x5-inch loaf pan with parchment paper. Add a layer of the ice cream mixture, followed by some of the diced fresh peaches and cobbler chunks. Repeat the layers until all the ingredients have been used, finishing with peaches and cobbler pieces on top. Cover the loaf pan tightly with foil and freeze for at least 8 hours, or until firm. Let the ice cream sit at room temperature for about 5 minutes before scooping and serving.