Prepare the tart dough first. Put the two flours, sugar and salt in food processor and pulse to combine. Add cold butter and pulse several times until mixture is slightly coarse with small chunks of butter. Add ice water slowly and pulse a few more times to incorporate. Check to see if dough holds together by squeezing. Place dough in plastic wrap and press into a circle. Chill for 1 hour. Heat oven to 350 degrees. Roll out dough into a rectangle on parchment about 1/4 inch thick. Transfer to a sheet pan. Chill for 15 minutes in freezer or refrigerator then brush with cream, or if you prefer an egg wash, and bake for 20-30 minutes until golden brown. Transfer to rack and let cool completely.
Toss cherries with 1-2 T of sugar (depending on how sweet the cherries are), 1 T lemon juice and a pinch of salt. Let sit at room temperature for 30 minutes or more. In a separate bowl, toss apricots with a little sugar depending on sweetness, 1 tsp lemon juice and a pinch of salt. Mix ricotta cheese with 1 T lemon zest.
To assemble, spread ricotta on cooled crust, top with cherries and apricots, sprinkle with toasted almonds and drizzle with honey. Cut into squares and serve. Serves 8-10.