Combine all ingredients in food processor. Pulse until mixture forms thick, coarse purée. Reserve.
For Pasta Dough
Combine all ingredients in stand mixer with dough hook. Mix at medium-low speed until mixture forms a cohesive dough and begins to separate from sides of bowl (about 8 minutes). Fold dough into ball, wrap in plastic, and let rest about 30 minutes. Roll pasta through pasta machine at least 3 times, starting at thickest setting and finishing at thinnest. Cut pasta into circles about 3 inches in diameter (a biscuit cutter or the edge of a downturned glass works for this). Spoon a tablespoon of pea mixture into center of pasta round, brush edges of pasta with egg wash, fold pasta into half-moon shape, brush the two end corners, and press together to make a crown shape. Makes a total of 12 tortellini.
Over high heat, bring pot of salted water to boil. Add tortellini gently to water and boil about 3 minutes, until just tender but toothsome (al dente). Drain, transfer into buttered sauté pan, and mix until well glazed with butter. Keep warm.
For Fennel and Artichoke Compote
Slice fennel and artichokes into long, thin slices. Warm olive oil in medium sauté pan over medium heat. Stir in fennel and artichoke, sautéing until soft (about 5 minutes). Add butter and thyme, and cook until vegetables are brown and caramelized in spots. Stir in lemon juice and cook until liquid evaporates. Season well with salt and pepper and keep warm.
For Arugula Coulis
Combine all ingredients in blender and purée until smooth.
Arrange 3 tortellini on center of each plate. Spoon equal portions of fennel-artichoke compote over each, and drizzle coulis around pasta. Serve immediately.
Note: Blanching Vegetables
Blanching sets the color of green vegetables. Make an ice-water bath in a large bowl by combining cold water with at least a half-dozen ice cubes. Bring a saucepan of water to a rapid boil. (Here you can use the same water for the peas and the arugula, but always blanch different vegetables in different batches; they cook at different rates.) Lower vegetables into boiling water. In this case, cook peas about 45 seconds, strain out with a large strainer, then plunge peas into ice water until chilled. Set aside on clean dishtowel to drain.
Add more ice cubes if all have melted. Return water to boil, if needed. Lower arugula into boiling water, pushing it down to cover it. Cook until just wilted (about 20 seconds). Corral it with the strainer and plunge it into ice water. When chilled, drain on towels.