Set a large sauté pan over medium-high heat and add 2 tbsp. oil. When the oil is shimmering, add the Swiss chard, onions, garlic, shallot sauce, and salt and pepper to taste, and sauté, stirring occasionally, until mixture is lightly caramelized and tender, 7-10 minutes. Transfer to a medium bowl and set aside until it’s cool to the touch, about 10 minutes.
Fill a small bowl with 1⁄2 cup water. Place 1 egg roll wrapper on a work surface with one corner pointing toward you—it should look like a diamond, not a square. Place about 1/3 cup chard mixture in a line across the center. Using a pastry brush (or your finger), lightly wet the edges of the egg-roll wrapper with water. Wrap the corner closest to you over the filling, fold in the two side corners, and then roll it away from you. Press the edges together to seal, adding more water if necessary. Repeat until you’ve used up the chard mixture—you should have about 8 egg rolls.
Set a large cast-iron pan over medium-high heat and fill with 1⁄2 inch oil. When the oil reaches 350°F, add egg rolls one at a time, taking care to not crowd the pan. Fry in batches if necessary. Cook, rotating them occasionally, until crispy and golden on all sides, 5–7 minutes. Remove to a plate lined with paper towels to drain, but serve soon, while they’re still hot.