Place a large metal bowl into the refrigerator to chill for at least 15-20 minutes. Meanwhile, add the sweetened condensed milk and 1 Tbsp of blackberry jam into a small bowl and whisk to combine. Set aside.
Remove the large chilled metal bowl from the refrigerator. Place a fine mesh sieve over the bowl and pour the lavender cream into it so that the lavender is strained from the cream. Press down on the lavender in the sieve to collect as much cream as possible, then discard the lavender.
Beat the strained lavender cream with a hand mixer (or using the whisk attachment on your stand mixer) on high speed until stiff peaks form, about 3 minutes.
Using a rubber spatula, fold one half of the sweetened condensed milk mixture into the heavy whipping cream mixture. When combined, gently fold in the rest of the sweetened condensed milk mixture in.
In an 9x5x3 inch loaf pan, add 1/2 of the lavender ice cream mixture. Add about half of the jam mixture by spoonfuls and swirl them into the ice cream with a skewer or butter knife. Add the rest of the lavender ice cream mixture and repeat the jam swirling process.
Cover the loaf pan with aluminum foil and freeze for 6-8 hours, after which it should be semi-firm, scoopable, and ready to enjoy!