Make the olive oil tart shell:
- Combine flour, sugar and salt in a large bowl. Whisk a bit to allow the salt and sugar to sift the flour.
- Whisk the olive oil and milk in a small bowl until the oil emulsifies.
- Make a well in the dry ingredients and pour the oil mixture into the flour. Mix gently with a fork until dry streaks disappear but dough is still crumbly. Do not over work.
- Turn out dough into pan. Use your hands to press out the dough to cover the bottom of the pan, pushing it up the sides to meet the edge, until about 1/8-inch thick. Trim and discard excess dough. Pastry is ready for use immediately – no need to chill.
- Line the shell with parchment parchment paper and fill with dried beans or pie weights. Bake at 350° Fahrenheit for 15 minutes, remove parchment paper and bake for 10 additional minutes. Remove from oven and let cool slightly.
Make olive oil lemon curd filling:
- While the tart shell is cooking, stir together the sugar, flour and table salt in a medium saucepan.
- Add the eggs, egg yolks, lemon zest and lemon juice. Stirring constantly, cook over medium-low heat until the mixture reaches 160° Fahrenheit on a kitchen thermometer. Mixture will thicken slightly.
- Remove from heat and strain into a bowl using a fine mesh sieve. Stir in olive oil until evenly mixed.
- Spoon filling into warm tart shell. Place tart pan onto a rimmed baking sheet and return to oven. Bake at 350° Fahrenheit for until set and just barely moves when the pan is shaken, about 8-10 minutes.
- Let cool completely before unmolding.
- Decorate with candied lemon slices (recipe below). Slice and serve, cleaning knife between cuts.
Make Candied Lemon Slices
- Line a rimmed baking sheet with parchment paper.
- Combine sugar, water and lemon juice in a large skillet. Heat on medium heat until sugar is dissolved.
- Add lemon slices in a single layer. Reduce heat to medium low and simmer about 15 minutes, flipping 1-2 times during the process. Slices will be soft and translucent.
- Lift slices from pan with a fork or tongs and let the sugar mixture drain off. Place on the waxed paper lined baking sheet. Allow to cool completely before arranging on lemon tart.
- Slices will keep in an airtight container in the fridge for 2-3 days.