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Bring milk, 6 tablespoons butter, 3/4 teaspoon kosher salt, dried mint, and dried oregano to a simmer in a medium saucepan over medium-high, stirring occasionally. Reduce heat to medium; add flour all at once, and stir rapidly using a wooden spoon until dough ball forms, pulls away from sides, and bottom of pan is clean, about 1 minute. Reduce heat to low, and cook, stirring constantly, until dough leaves film on bottom and sides of pan and no longer steams, 4 to 5 minutes.
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Place dough in bowl of a stand mixer fitted with the paddle attachment. Add mustard, herbs, and fennel; beat on medium-low speed until combined, about 10 seconds. Add feta, and beat on medium-low speed until combined, about 10 seconds. With mixer running on medium-low speed, add eggs, 1 at a time, beating until incorporated after each addition. Increase mixer speed to high, and beat until dough is soft, smooth, and sticky, about 2 minutes. Transfer dough to a disposable pastry bag; tie top of bag using kitchen twine. Refrigerate dough 1 hour.
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Line a large rimmed baking sheet with parchment paper. Bring a large saucepan of water to a vigorous simmer over high. Reduce heat to medium-low to maintain a very gentle simmer. Cut the end off the tip of pastry bag to create a 3/4-inch opening. Working in about 4 batches (about 30 batter pieces per batch), pipe dough straight down, just above simmering water, cutting dough at 1-inch lengths using a paring knife or scissors. Adjust heat as needed to maintain a gentle simmer. Once gnocchi rise to surface, simmer over medium-low, undisturbed, until very soft and just set, 1 to 2 minutes per batch. Using a spider strainer or slotted spoon, remove gnocchi, draining as much water as possible before transferring to prepared baking sheet in a single layer. Repeat process with remaining dough. Cover baking sheet with plastic wrap, and refrigerate until firm, at least 30 minutes or up to 1 day.
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Whisk together yogurt, lemon zest and juice, garlic, and remaining 1/4 teaspoon kosher salt in a medium bowl; set aside.
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Working in 2 batches, heat 1 tablespoon oil and 2 tablespoons butter in a large nonstick skillet over high until sizzling, about 3 minutes. Add half of the gnocchi (about 21/2 cups); cook, tossing and gently stirring often, until golden brown in spots, 3 to 5 minutes. Transfer gnocchi to a large plate; cover with aluminum foil to keep warm. Repeat process with remaining 1 tablespoon oil, remaining 2 tablespoons butter, and remaining gnocchi.
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To serve, divide yogurt mixture evenly among 4 plates; top evenly with gnocchi. Sprinkle with peas. Garnish with fresh herbs, flaky sea salt, and crushed red pepper.