Prepare the lemon. Wash and dry the lemon. Finely grate the zest without the bitter white pith, cover it, and refrigerate until serving. Measure the lemon juice separately for the syrup.
Dissolve the syrup. Combine the water, poaching sugar, vanilla or vanillin sugar, and lemon juice in the wide pot. Bring to a boil, stirring until the sugar dissolves, then reduce the heat for a quiet poach.
Peel and core. Wash and peel the apples. Remove the cores carefully with a small knife or corer to make cavities about 1–1¼ inches (2.5–3 cm) across. Leave an intact base and substantial walls so the apples hold their filling. Do not push a corer straight through.
Poach gently. Lower the prepared apples into the syrup promptly. Arrange upright in one layer; the syrup should reach at least two-thirds of their height. Cover and maintain a very gentle simmer, not a rolling boil. Turn the apples carefully every 2–3 minutes so they cook evenly. For larger batches, use additional suitable pots rather than crowding one.
Check the fruit. Begin checking around 10 minutes; poaching commonly takes 10–12 minutes, with very firm apples sometimes needing another 1–2 minutes. A thin skewer should enter the flesh with slight resistance while the apple still holds its shape. Check individual apples if they entered the pot at different times. Lift each out as soon as ready; they continue to soften while cooling.
Lift without breaking. Support each apple from underneath with a slotted spoon. Set upright in a shallow dish and let excess syrup drain away. Avoid gripping the softened walls or stacking the apples.
Divide the prepared syrup. Measure a total of 1.25 cups (300 ml) of syrup from the poaching pot. Set aside 0.25 cup (60 ml) while warm for the filling and 1 cup (240 ml) for cooling and serving. These portions are taken from the original syrup, not added on top of it. The metric volumes are the precise reference; cup measures are rounded.
Mix the filling. Combine the ground walnuts and filling sugar. Stir in the reserved warm filling portion of syrup gradually, using the measured amount. The mixture should be moist and moldable, with no puddle of syrup. Let it cool before placing it in the apples.
Cool the components. Let the apples and filling cool until no longer warm, and cool the reserved serving syrup completely in a separate shallow container. Allow approximately 30 minutes for initial cooling; actual time varies. An ice bath around the syrup container can speed this up. Refrigerate shallow containers promptly if cooling takes longer; do not leave the components out for more than 2 hours, or 1 hour above 90°F (32°C). Keep the cream refrigerated.
Fill the apples. Divide the cooled walnut filling among the cooled apples, packing gently into each cavity and leaving a small mound on top. Arrange upright in a shallow serving dish or individual bowls. Pour the fully cooled reserved serving syrup around the apples, keeping the filling above the liquid.
Chill thoroughly. Cover and refrigerate at 40°F (4°C) or below for at least 2 hours, until the apples, filling, and syrup are thoroughly chilled. Keep refrigerated until serving; this step follows the initial cooling period.
Whip the cream. Just before serving, whip the cold heavy cream in a chilled bowl until it holds firm peaks. Stop before it becomes grainy. Do not add cream to the walnut filling in this version.
Finish and serve. Divide the whipped cream over the apples. Top each serving with its walnut-half garnish and a little reserved lemon zest. Serve cold with the measured serving syrup divided among the portions. Refrigerate leftovers promptly.