In a large skillet or sauté pan, heat 2 tablespoons olive oil over medium heat. Add the shallots and garlic and cook until the onion is soft, around 5 minutes. Add artichoke hearts and white wine, reduce heat to medium-low and continue cooking, stirring occasionally, until liquid evaporates, around another 5 minutes. Remove from heat and stir in sundried tomatoes, parsley, basil and thyme. Set aside to cool.

Using an electric mixer with the whisk attachment, blend the ricotta cheese until smooth. Blend in eggs until incorporated. Stir in Asiago cheese, 2 tablespoons Parmesan cheese and cooled artichoke mixture. Season to taste with salt and pepper. Set aside.

In a small mixing bowl, stir together the ground almonds and remaining 1/3 cup Parmesan cheese. Set aside.

Preheat oven to 375 degrees. Line a large rimmed cookie sheet with parchment paper.

Place one sheet of phyllo on work surface. (Cover remaining sheets with waxed paper and then a damp dish cloth to keep phyllo from drying out.) Brush single sheet with olive oil and sprinkle with 1 1/2 tablespoons of the almond-Parmesan mixture. Continue layering phyllo sheets, brushing with oil and sprinkling with nuts, for a total of 5 layers.

Spread half of the artichoke mixture in a strip, along one of the long sides of the phyllo stack, leaving a 1-inch border. Starting with the artichoke mixture side, roll up into a log. Brush with olive oil and place on prepared cookie sheet, seam side down.

Repeat process with remaining phyllo sheets, almond mixture and artichoke filling. Place the second log on baking sheet next to the first log. Make 8 diagonal cuts on top of each one, not quite all the way through the phyllo. Bake for 30 to 40 minutes, or until golden brown and crispy. Remove from oven and let sit 5 to 10 minutes. Slice along cuts and serve.